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THE  LIBRARY 

OF 
THE  UNIVERSITY 

OF  CALIFORNIA 

PRESENTED  BY 

PROF.  CHARLES  A.  KOFOID  AND 
MRS.  PRUDENCE  W.  KOFOID 


Eli 


THE  LIBRARY 

OF 

THE  UNIVERSITY 
OF  CALIFORNIA 


PRESENTED  BY 
^ROF.  CHARLES  A.  KOFOID  AND 


<RS.  PRUDENCE  W.  KOFOID 


LONDON. 

NEW 
PR: 


A       GREEK 

**  English -Gn; 
of  Colleges  and 
A.  GILES,  LL  D 
Oxon ;  Head  M£ 
School.  In  one 
One  Guinea,  cloi 

The  object   of 
reduce  into  a  sma 
able  price,  for  the 
the  best  in  for  mat 
found  hitherto  ij 
With  this  view  I 
tents  of  the  G 
small  a  space  (at 
larger   number 
volume  of  the  sa 
for  the  introducti 
Lexicon  at  least  tw 
any   that   has  yet  a 
second  part  will  be 
particle  of  informatiot 
cured  from  other  Lexi 
tity  besides.     A  short 
prefixed,  which  may  be 
who  do  not  wish  to  mult 
be  glad  to  find  the  present 
for  two  purposes, 

"  This  is  a  worthy  companion  to  Riddle's 
Latin  Dictionary,  containing  all  the  informa- 
tion necessary  to  a  student;  and,  what  is  of 
equal  importance,  no  more.  The  author  is 
generally  successful  in  developing  the  struc- 
ture and  composition  of  the  Greek  language; 
avoiding  the  quibbling  derivations  which  dis- 
figure the  older  lexicons,  and  especially  that 
of  Schrevelius,  he  points  out  the  genuine 
radicals  so  far  as  they  can  be  discovered  with 
certainty." — Athenaeum. 

TONGINUS    ON    THE    SUBLIME; 

chiefly  from  the  Text  of  Weiske,  with 
copious  English  Explanatory  Notes,  and 
Indexes;  and  Life  of  Longinus.  By  D.  B. 
HICKIE,  LL.D  ,  Head  Master  of  Hawks- 
head  Grammar  School,  Editor  of  Livy,  &c. 
1  vol.  post  8vo.  5s.  cloth  lettered. 

"  The  notes  evince  sound  judgment,  ex- 
tensive reading,  and  correct  taste." — Monthly 
Review. 

By  the  same  Editor, 

SELECT  IDYLLS  of  THEOCRITUS; 
comprising  the  first  Eleven,  the  15th,  18th, 
19th,  20th,  and  24th.  From  the  Text  of 
Meineke,  with  copious  English  Notes, 
Grammatical  and  Explanatory  References, 
&c.  1  vol.  post  8vo,.  6s.  cloth  lettered. 


try    3.6,    184O. 

ETC. 

)   CO. 

LISH    LEXICON 

stament ;  especially 
olleges  and  the  higher 
Schools  ;  but  also  in- 
;  Manual  for  Biblical 

By  the  Rev.  S.   T. 

S.A.  1  volume,  fcp. 
ered. 

e  Author, 

ESTAMENT,  with 
,  Critical,  Philologi- 
3d  edition,  greatly 
iderably  improved,  in 
imes,  8vo.,  with  Map 
landsomely  bound  in 


jdition  of  the  Greek 
valuable  that  has  yet 
iress  in  this  country  ; 
all  those  whose  pro- 
ose  leisure  admits  of, 
sacred  writings.     Dr. 
>th  of  the  Church  and 
and  has  fairly  earned 
tion   which    the   dis- 
.1  patronage   have  to 
bestow." — Eclectic  Review. 

"  Much  as  had  been  done  in  the  two  pre- 
ceding impressions,  the  third  edition  is  yet 
further  enlarged  and  very  materially  im- 
proved. In  addition  to  his  own  researches, 
Dr.  Bloomfield  has  availed  himself  of  various 
suggestions  for  the  improvement  of  his  work, 
which  in  its  present  state  exhibits  the  results 
of  the  labours  of  all  preceding  critical  editors 
of  the  New  Testament,  as  well  as  of  his  own 
researches  for  more  than  thirty  years.  .  . 
Upon  the  whole,  without  depreciating  the 
merit  of  the  labours  of  preceding  editors, 
this  third  edition  may  justly  be  regarded  as 
the  most  valuable  for  Biblical  students  that 
has  yet  been  issued  from  the  press  in  this 
country." — Rev.  T.  Hartwell  Home's  Intro- 
duction to  the  Holy  Scriptures,  9th  edit.  1839. 

COLLEGE  and   SCHOOL    GREEK 

Testament,  with  English  Notes.  Second 
Edition,  with  Additions,  and  a  new  Map  of 
Palestine,  adapted  to  the  Gospel  History. 
1  thick  vol.,  12mo.  10s.  6d.  cloth  lettered. 

"  This  edition  of  the  Greek  Testament 
supplies  a  desideratum  in  scholastic  litera- 
ture. The  Notes  (which  are  strictly  gram- 
matical, scholastic,  and  elementary)  furnish 
to  the  juvenile  student  every  requisite  aid 
for  the  correct  interpretation  of  the  New 
Testament." —  Christian  Remembrancer. 


LONGMAN,    OR.XKE, 


CO.'S    X.IST 


A  COMPLETE  LATIN  DICTION- 
**  ary.  By  the  Rev.  J.  E.  RIDDLE,  M.A. 
In  one  thick  volume,  8vo.  Price  One 
Guinea,  cloth  lettered. 

By  the  same  Author, 
A   COMPLETE   ENGLISH-LATIN 
Dictionary.     One  volume,  8vo.  price  lOs.Gd. 
cloth  lettered. 

The  above  may  be  had  bound  together  in 
one  volume. 

Also, 

AN  ABRIDGMENT  of  the  ABOVE, 
for  the  use  of  Schools  Price  12s.  bound. 

The  Latin-English  (7s.)  and  English- 
Latin  (5s.  6d. )  Portions  may  be  had  sepa- 
rately. 

"  Riddle's  Complete  Dictionary  is  the  best 
of  its  kind  in  our  language,  and  we  rejoice 
to  hear  that  in  our  provincial  schools  it  is 
fast  superseding  all  others.  The  Abridg- 
ment is  a  careful  condensation  of  the  ori- 
ginal."— Athenaeum. 

"  By  far  the  most  judiciously  condensed 
School  Dictionary  I  have  ever  met  with,  and 
by  its  clear  exposition  of  the  primary  mean- 
ing of  words,  leads  the  student  to  the 
secondary  and  metaphorical  ones  with  ad- 
mirable judgment  and  good  taste.  I  con- 
sider it  as  a  very  able,  and  1  may  add,  a  very 
philosophical  work."— Extract  from  a  letter 
from  the  late  Bishop  of  Lichfield  and  Coventry 
to  the  Publishers. 

THE      NEW     ETON     GREEK 

Grammar;  or  the  Eton  Grammar  in 
English:  and  the  Latin  Rules  of  Syntax  and 
Prosody  arranged  with  the  English  in  paral- 
lel columns;  with  many  important  additions, 
together  with  Practical,  Analytical,  and  Phi- 
losophical Notes.  By  CLEMENT  MOODY,  of 
Magdalen  Hall,  Oxford,  late  one  of  the 
Masters  of  TunbrSdge  School,  and  Editor  of 
the  Eton  Latin  Grammar  in  English.  One 
volume,  12mo.,  price  4s.  cloth  lettered. 

In  this  Grammar  are  followed  out  the 
simplified  plan  and  easy  principles  of  the 
New  Eton  Latin  Grammar.  The  analogy 
between  the  two  languages  is  developed, 
chiefly  from  the  elaborate  work  of  Vossius ; 

\    and  the  Notes  have  been  carefully  selected 
and    condensed    from    Matthias,    Thiersch, 

<    Buttman,  and  other  learned  grammarians. 

.  LINGUIST"  A   COMPLETE 

Course  of  Instructions  in  the  German 
Language;  in  which  attention  is  particularly 
directed  to  peculiarities  in  Grammatical 
Forms  and  Construction.  Exemplified  by 
selections  from  the  best  Authors.  By  D. 
BOIIEAU,  Author  of  "The  Nature  and 
Genius  of  the  German  Language/'  &c.  &c 
New  edition,  carefully  revised  and  corrected 
1  vol.  I2mo.,  price  7s.  cloth. 


THE 

•*• 


REEK   VOCABULARY;    OR, 

Exercises  on  the  Declinable  Parts  of 
Speech.  By  the  Rev.  J.  R.  MAJOR,  D.D. 
Head  Master  of  the  King's  College  School, 
London.  Second  edition,  corrected  and 
enlarged,  12mo.  2s.  6d.  cloth  lettered. 

Advertisement  to  the  Second  Edition. 
<  The  plan  and  design  of  this  publication 
having  been  approved,  no  pains  have  been 
spared   to  render  the  second  edition  better 
adapted  to  the  object  which  it  professes  to 
have  in  view.     The  work  has  been  consider- 
ably enlarged  by  the  addition  of  new  words  ; 
thus  supplying  a  more  copious  fund  of  ex- 
amples under  the   several  forms  of  declen- 
sion and  conjugation,  and  (in  consequence 
of  the  alphabetical  arrangement)   compen- 
dious   tables   of  reference    to    the    primary 
meanings   of  roots    or    words   of    ordinary     j 
occurrence.      A   few   simple  exercises  have    ; 
been  subjoined,  intended  principally  to  serve    i 
as  hints  of  the  uses  to  which  the  materials    ; 
here  furnished  may  be  applied  in  tuition." 

THE  ANABASIS  OF  XENOPHON; 

chiefly  according  to  the  Text  of  HUTCH- 
INSON.  With  Explanatory  Notes  and  Illus- 
trations of  Idioms  from  Viger,  &c.,  copious 
Indexes,  and  Examination  Questions.  By 
F.  CUNNINGHAM  BELFOUR,  M  A.  Oxon. 
F.R.A.S.  LL.D.,  late  Professor  of  Arabic 
in  the  Greek  University  of  Corfu.  Third 
edition,  with  corrections  and  improvements, 
post  Svo.,  8s.6d.  boards. 

In  preparing  this  Third  Edition  for  the 
use  of  the  public,  great  care  has  been  taken 
to  revise  the  whole  of  the  text  on  the  several 
foreign  texts  of  Bornemann,  Poppo,  Din- 
dorf,  and  Negris.  By  the  judgment  of  the 
last,  himself  a  native  Greek,  the  Editor  has 
been  much  guided  in  his  adoption  of  various 
improvements.  Some  recommendation  of 
the  present  over  former  editions  will  be 
found  in  the  English  language  of  the  index 
to  the  words  and  phrases,  by  conversion 
from  the  Latin  ;  and  in  the  augmentation  of 
the  indices  to  the  notes  by  sundry  additional 
forms  both  of  grammar  and  rhetoric. 

T>OBINSON'S  GREEK  AND  ENG- 
•**  lish  Lexicon  of  the  New  Testament. 
Edited,  with  careful  revision,  corrections, 
occasional  additions,  and  a  preface,  by  Dr. 
BLOOMFIELD.  1  vol.  Svo.  price  18s.  cloth. 

"  Dr.  Robinson's  Lexicon,  as  edited  by 
Dr.  Bloomfield,  must  prove  of  great  value 
to  every  student  who  is  wise  enough  to  pro- 
cure it." — BRITISH  CRITIC  AND  QUARTERLY 
THEOLOGICAL  REVIEW. 

"  We  consider  this  the  best  Lexicon  of  the 
Greek  Testament  that  is  extant. — CHURCH 
OF  ENGLAND  QUARTERLY  REVIEW. 


OF     WEW     PUBLICATIONS     FOR    COLLEGES. 


A      GUIDE     TO     THE     READING 

"  of  the  Greek  Tragedians ;  being  a 
series  of  articles  on  the  Greek  Drama, 
Greek  Metres,  and  Canons  of  Criticism. 
Collected  and  arranged  by  the  Rev.  J.  R. 
MAJOR,  D.D.,  Head  Master  of  King's 
College  School,  London,  8vo.  7s.  6d.  bds. 

In  this  manual  the  editor  has  endeavoured 
to  bring  together,  from  various  sources,  in- 
formation both  interesting  and  useful  to  the 
student  on  the  several  heads  of  the  Greek 
Drama,  Greek  Metres,  and  Canons  of  Cri- 
ticism. On  the  first  head,  extracts  have 
been  given  from  Bentley's  Dissertation  on 
Phalaris,  as  the  chief  authority  for  the  age 
of  Thespis,  and  the  origin  of  Tragedy  and 
Comedy  ;  care  having  been  taken  to  divest 
them  of  sucli  controversial  allusions  and 
digressions  as  might  embarrass  the  reader  in 
his  investigations.  These  extracts  are  suc- 
ceeded by  others  from  Cumberland's  Obser- 
ver, Francklin's  Preface  to  Sophocles,  Twi- 
ning's  Aristotle,  Clinton's  Fasti  Hellenici, 
and  other  authors  to  whom  references  are 
made,  on  the  Progress  of  the  Drama,  the 
History  and  Comparative  Merits  of  the 
principal  Tragic  and  Comic  Writers,  and 
the  Construction  of  the  Greek  Theatre.  On 
the  subject  of  Metres,  the  Editor  had  pre- 
fixed an  introduction  to  his  edition  of  the 
Hecuba  of  Euripides,  which  he  had  been 
frequently  requested  to  publish  in  a  separate 
form,  for  the  purpose  of  reference  in  the 
reading  of  Greek  Plays  generally.  With 
that  view  it  is  here  reprinted,  and  at  the 
same  time  considerably  enlarged  by  the  aid 
of  Elmsley's  review  of  Person's  Hecuba, 
Seager's  Translation  of  Hermann  on  Metres, 
and  Prof.  Dunbar's  able  Exposition  of  the 
Ictus  Metricus.  The  pages  of  the  Classical 
Journal  have  supplied  many  of  the  articles 
<  of  which  the  Editor  has  availed  himself,  and 
in  particular  the  abstract  of  Canons  from 
Porson's  Euripides,  Blomfield's  ./Eschylus, 
and  Monk's  Hippolytus  and  Alcestis.  The 
principle  criticisms  from  Dawe's  Miscellanea 
Critica,  and  a  translation  from  the  German 
of  C.  G.  Haupt,  on  the  Dialect  of  the  Tra- 
gedians, conclude  this  miscellany. 


TTURIPIDES.  FROM  THE  TEXT, 
and  with  a  Translation  of  the  Notes,  Pre- 
face,  and  Supplement  of  Porson  ;  Critical  and 
Explanatory  Remarks,  original  and  selected ; 
Illustrations  and  Idioms  from  Matthiae, 
Daws,  Viger,  etc. ;  and  a  Synopsis  of  Metrical 
Systems.  By  Dr.  MAJOR,  Head  Master 
of  King's  College  School.  1  vol.  post  8vo. 
price 24s.  cloth.  Sold  separately  as  follow  : — 
Alcestis,  Hecuba,  Medea,  Orestes,  Phos- 
,  5s.  each. 


QOPHOCLES,    COMPLETE:    FROM 

the  Text  of  Hermann,  Brunck,  etc  with 
original  Explanatory  English  Notes,  Ques- 
tions, and  Indexes.  By  Dr.  BRASSE,  Mr. 
BURGES,  and  the  Rev.  F.  VAI.PY. — 2vols.  post 
8vo.  84s.  cloth.  Sold  separately  as  follow  :  — 
OZdipus  Rex,  OZdipus  Coloneus,  Antigone, 
Trachiniae,Philoctetes,  Ajax,Electra,5s.each. 

r<  ATULLUS  JUVENALIS,  PERSIUS 

Expurgati.     In   usum  Scholae  Harro- 

viensis.     1  vol.  fcp.  8vo.  5s.  cloth  lettered. 

Although    the    text    is    expurgated,    the 

established  number  of  the  lines  is  retained, 

in  order  to  facilitate  the  reference  to  the 

notes  in  other  editions. 

GCHOOL  BOTANY;    OR,   AN    EX- 

planation  of  the  Characters  and  Differ- 
ences of  the  Principal  Natural  Classes  and 
Orders  of  Plants,  belonging  to  the  Flora  of 
Europe,  in  the  Botanical  Classification  of 
De  Candolle.  For  the  use  of  Students  pre- 
paring for  their  Matriculation  Examination 
in  the  University  of  London.  By  JOHN 
LINDLEY,  Ph.  D.,  F.R.S  L.,  &c.,  Professor 
of  Botany  in  the  London  University  College, 
and  in  the  Royal  Institution.  1  vol.  fcp. 
8vo.  illustrated  with  upwards  of  160  wood- 
cuts, price  6s.  cloth  lettered. 

T^HE  BIOGRAPHICAL  TREASURY; 

containing  Memoirs,  Sketches,  or  brief 
Notices  of  the  Lives  of  about  12,000  Emi- 
nent Persons,  from  the  earliest  periods  of 
history  to  the  present  day.  By  S.  MAUNDER. 
2d  Edition,  8s.  6d.  cloth  ;  10s.  6d.  roan  gilt. 

"  An  extraordinary  book,  whether  we 
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piled production  of  the  sort  which  has  pro- 
bably ever  issued  from  the  press." — GLOBE. 

THE  TREASURY  OF  KNOW- 
ledge;  comprising  an  English  Dictionary, 
an  English  Grammar,  a  Universal  Gazetteer, 
a  Classical  Dictionary,  a  Chronological  Ana- 
lysis of  General  History,  a  Dictionary  of 
Law  Terms,  etc.  etc.  llth  edit,  revised 
and  greatly  enlarged,  8s.  6d.  cloth ;  10s.  6d. 
roan  gilt. 

"  We  have  here,  in  a  form  admirably 
adapted  for  the  traveller's  portmanteau,  the 
most  complete  and  generally-useful  publica- 
tion which  it  has  ever  fallen  to  our  lot  to 
notice." — ATHENJEUM. 

By  the  same  Author,  (in  the  Press,) 

THE  SCIENTIFIC  AND  LITE- 
rary  Treasury.  A  New  Dictionary  of  the 
Arts  and  Belles  Letters. 


X.ONG1KA17,    ORIVTS,    A3MD     CO.'S    IiIST. 


ILLUSTRATIONS    OF    SCIENCE 

•by  Professors  of  King's  College,  Lon- 
don :  forming  a  Course  of  Instruction  in 
Natural  Philosophy  and  Natural  History, 
by  the  Method  of  Illustration. 

VOLUME  I.     MECHANICS. 
By  the  Rev.    H.  MOSELEY,  M.A.,   F.R.S., 
Professor  of  Natural  Philosophy  and  Astro- 
nomy  in    King's    College.     Fcp.   8vo.  8s. 
cloth  lettered. 

The  following  are  in  preparation  : 
ILLUSTRATIONS  OF   ZOOLOGY. 
2  vols.      By  THOMAS  BELL,  F.R.S. 

ILLUSTRATIONS  OF  EXPERI- 
mental  Philosophy.  2  vols.  By  C.  WHEAT- 
STONE,  F.R.S. 

ILLUSTRATIONS  OF  ANIMAL 
Physiology.  By  R.  B.  TODD,  M.D.  F.R.S. 

ILLUSTRATIONS  OF  HYDRO- 
statics  and  Hydrodynamics.  By  the  Rev. 
H.  MOSELEY,  M.A.  F.R.S. 

ILLUSTRATIONS  OF   NATURAL 

Products  useful  in  the  Arts  and  Manufac- 
tures. By  J.  F.  ROYLE,  M.D.,  Vice -Pre- 
sident of  the  Royal  Society. 

ILLUSTRATIONS  OF  BOTANY 
and  Vegetable  Physiology,  Astronomy,  Phy- 
sical Geography,  &c. — will  follow  in  succes- 


AN  INTRODUCTION  TO  THE 
Theory  and  Practice  of  Plane  and 
Spherical  Trigonometry,  and  the  Stereo- 
graphic  Projection  of  the  Sphere  ;  including 
the  Theory  of  Navigation :  comprehending 
a  variety  of  Rules,  Formulae,  &c.,  with  their 
Practical  Applications  to  the  Mensuration 
of  Heights  and  Distances  \  to  determine  the 
Latitude  by  two  Altitudes  of  the  Sun,  the 
Longitude  by  the  Lunar  Observations,  and 
to  other  important  Problems  on  the  Sphere, 
and  on  Nautical  Astronomy.  By  THOMAS 
KEITH.  Seventh  edition,  corrected  and  im- 
proved, by  Samuel  Mayuard.  8vo.  14s. 
cloth  lettered. 

The  present  edition  has  undergone  several 
important  changes,  and  the  work  is  now 
given  in  a  form  more  in  accordance  with  the 
modern  state  of  the  science.  Various  in- 
vestigations and  demonstrations  have  been 
pruned  and  remodelled,  some  important 
errors  corrected,  and  the  notations  and 
enunciations  throughout  improved.  The 
astronomical  problems  have  been  made  to 
depend  for  their  data  on  the  Nautical  Al- 
manac for  1840.  The  logarithms,  &c.  are 
all  given  in  full,  instead  of  having  their 
leading  figures  suppressed  as  in  former  edi- 
tions. This  arrangement  gives  to  the  com- 


puter a  greater  facility  and  confidence  in 
the  use  of  tables,  and  has  in  consequence 
been  adopted.  The  examples  and  numerical 
operations  have  all  been  carefully  examined, 
so  that  few  errors  of  consequence  are  likely 
to  have  escaped. 

By  the  same  Author, 
THE  ELEMENTS  OF  PLANE 
Geometry  :  containing  the  first  Six  Books  of 
Euclid.  From  the  Text  of  Dr.  Simson; 
with  Notes  Critical  and  Explanatory.  To 
which  are  added,  Book  7,  including  several 
important  propositions  which  are  not  in 
Euclid;  together  with  the  Quadrature  of 
the  Circle,  the  Lune  of  Hippocrates,  the 
Maxima  and  Minima  of  Geometrical  Quan- 
tities, &c. ;  and,  Book  8,  consisting  of  Prac- 
tical Geometry  :  also,  Book  9,  of  Planes  and 
their  Intersections;  and  Book  10,  of  the 
Geometry  of  Solids.  Fourth  edition,  cor- 
rected and  improved,  by  S.  Maynard.  8vo. 
10s.6d.  boards. 

Also,  by  the  same  Author, 
A  NEW  TREATISE  ON  THE  USE 
of  the  Globes ;  or  a  Philosophical  View  of 
the  Earth  and  Heavens  :  comprehending  an 
account  of  the  figure,  magnitude,  and  motion 
of  the  Earth  ;  with  the  natural  changes  of 
'its  surface,  caused  by  Floods,  Earthquakes, 
&c.,  together  with  the  Principles  of  Meteor- 
ology, and  Astronomy;  with  the  Theory  of 
the  Tides,  &c.  Preceded  by  an  extensive 
selection  of  Astronomical  and  othej-  Defini- 
tions, &c.  &c.  New  edition,  considerably 
improved,  by  J.  Rowbotham,  F.  R.A.S. 
12mo.,  with  seven  Plates,  price  6s- 6d.  bound. 
%*  In  this  edition  are  introduced  many 
new  questions  relating  to  the  positions  of  the 
Sun,  Moon,  and  Planets,  for  the  years 
1838,  1839,  1840,  1841,  and  1842,  respec- 
tively. 

KEY,  by  Prior,  2s.  6d.  cloth. 

CABLES     OF     SIX-FIGURE 

Logarithms ;     containing    the     Loga- 

ithms  of  Numbers  from  1  to  10,000,  and  of 

Sines  and  Tangents  for  every  Minute  of  the 

Quadrant  and  every  Six  Seconds  of  the  first 

Two  Degrees.     To  which  are  added,  a  Table 

of  Constants,  and  Formulae  for  the  Solution 

of  Plane  and  Spherical  Triangles. 

Superintended  by  Richard  Farley,  of  the 
Nautical    Almanac    Establishment.      (Just 


#*  The  Works  in  the  present  Catalogue 
are  a  selection  from  the  Publishers'  General 
School  Catalogue,  comprising  only  the 
newest  Works,  and  also  a  few  new  Editions. 
The  General  Catalogue,  including  Mr. 
Valpy's  extensive  series  of  Greek  and  Latin 
Works,  will  be  sent  by  Post  (free)  to  any 
person  applying  for  it. 


London:    Printed  by  Manning  and  Mason,  12,  Ivy-lam 


THE 


PHILOSOPHY 


OF   THE 


INDUCTIVE    SCIENCES, 


FOUNDED  UPON  THEIR  HISTORY. 


BY  THE 

REV.  WILLIAM  WHEWELL,  B.D., 

KliLLOW  Ofr    TRINITY  COLLKGE,    AND   PROFESSOR  OF   MORAL   PHILOSOPHY   IN    THE   UNIVERSITY 

OF    CAMBRIDGE,   VICE-PRESIDENT  OF  THE   GEOLOGICAL  SOCIETY 

OF   LONDON. 


IN  TWO  VOLUMES. 


VOLUME  THE  FIRST. 


LONDON: 

JOHN   W.   PARKER,    WEST   STRAND. 
CAMBRIDGE :  J.  AND  J.  J.  DEIGHTON. 


M.DCCC.XL. 


LONDON  : 

HARRISON  AND  Co.,  POINTERS, 
ST.  MARTIN'S  LANK. 


TO   THE 

REV.  ADAM  SEDGWICK,  M.A., 

SENIOR    FELLOW    OF    TRINITY   COLLEGE, 

WOODWARDIAN  PROFESSOR  OF  GEOLOGY  IN  THE  UNIVERSITY  OF 
CAMBRIDGE,  AND  PREBENDARY  OF  NORWICH. 


MY  DEAR  SEDGWICK, 

When  I  showed  you  the  last  sheet  of  my  History  of  the  In- 
ductive Sciences  in  its  transit  through  the  press,  you  told  me  that 
I  ought  to  add  a  paragraph  or  two  at  the  end,  by  way  of  Moral 
to  the  story ;  and  I  replied  that  the  moral  would  be  as  long  as 
the  story  itself.  The  present  work,  ihe  Moral  which  you  then 
desired,  I  have,  with  some  effort,  reduced  within  a  somewhat 
smaller  compass  than  I  then  spoke  of;  and  I  cannot  dedicate  it 
to  any  one  with  so  much  pleasure  as  to  you. 

It  has  always  been  my  wish  that,  as  far  and  as  long  as  men 
might  know  anything  of  me  by  my  writings,  they  should  hear  of  me 
along  with  the  friends  with  whom  I  have  lived,  whom  I  have  loved, 
and  by  whose  conversation  I  have  been  animated  to  hope  that  I 
too  might  add  something  to  the  literature  of  our  country.  There 
is  no  one  whose  name  has,  on  such  grounds,  a  better  claim  than 
yours  to  stand  in  the  front  of  a  work,  which  has  been  the  subject 
of  my  labours  for  no  small  portion  of  our  long  period  of  friend- 
ship. But  there  is  another  reason  which  gives  a  peculiar  pro- 
priety to  this  dedication  of  my  Philosophy  to  you.  I  have  little 
doubt  that  if  your  life  had  not  been  absorbed  in  struggling 
with  many  of  the  most  difficult  problems  of  a  difficult  science, 
you  would  have  been  my  fellow-labourer  or  master  in  the  work 
which  I  have  here  undertaken.  The  same  spirit  which  dictated 
your  vigorous  protest  against  some  of  the  errors  which  I  also 
attempt  to  expose,  would  have  led  you,  if  your  thoughts  had  been 
more  free,  to  take  a  leading  share  in  that  Reform  of  Philosophy, 

a  2 


7832 


iv  DEDICATION. 

which  all  who  are  alive  to  such  errors,  must  see  to  be  now  indis- 
pensable. To  you  I  may  most  justly  inscribe  a  work  which  con- 
tains a  criticism  of  the  fallacies  of  the  ultra-Lockian  school. 

I  will  mention  one  other  reason  which  enters  into  the  satisfac- 
tion with  which  I  place  your  name  at  the  head  of  my  Philosophy. 
By  doing  so,  I  may  consider  myself  as  dedicating  it  to  the  College 
to  which  we  both  belong,  to  which  we  both  owe  so  much  of  all 
that  we  are,  and  in  which  we  have  lived  together  so  long  and^so 
happily ;  and  that,  be  it  remembered,  the  College  of  Bacon  and  of 
Newton.  That  College,  I  know,  holds  a  strong  place  in  your  affec- 
tions, as  in  mine ;  and  among  many  reasons,  not  least  on  this 
account ; — we  believe  that  sound  and  enduring  philosophy  ever 
finds  there  a  congenial  soil  and  a  fostering  shelter.  If  the  doc- 
trines which  the  present  work  contains  be  really  true  and  valu- 
able, my  unhesitating  trust  is,  that  they  will  spread  gradually 
from  these  precincts  to  every  part  of  the  land. 

That  this  office  of  being  the  fosterer  and  diffuser  of  truth  may 
ever  belong  to  our  common  Nursing  Mother,  and  that  you,  my 
dear  S^dgvvick,  may  long  witness  and  contribute  to  these  bene- 
ficial influences,  is  the  hearty  wish  of 

Yours  affectionately, 

W.  WHEWELL. 
Trinity  College,  May  1,  1840. 


CONTENTS 


OF 


THE    FIRST    VOLUME. 


Page 

PREFACE           .......  ix 

Aphorisms  respecting  Ideas              ....  xvii 

Aphorisms  respecting  Knowledge          ....  xxxvii 

Aphorisms  respecting  the  Language  of  Science       .             .  xLviii 

Aphorism  I.  relative  to  the  Ancient  Period             .             .  xLix 

1.  Common  Words          .             .             .  XLIX 

2.  Descriptive  Terms               .             .             .             .  Lii 

3.  Theoretical  Terms       ....  Liv 
Aphorism  II.  relative  to  the  Modern  Period           .             .  Lix 

1.  Systematic  Nomenclature        .             .  LX 

2.  Systematic  Terminology     ....  Lxi 

3.  Systematic  Modification          .             .             .  LXIV 
Aphorisms  (III.,  IV.,  V.,  VI.,  VII.,)  relative  to  the  Ap- 
propriation of  Common  Words            .             .             .  Lxvii 

Aphorisms  (VIII.,  IX.,  X.,  XI.,  XII.,  XIII.,  XIV.,) 

relative  to  the  Construction  of  New  Terms         .  Lxxiii 

Aphorism  XV.,  relative  to  the  Form  of  Terms       .             .  xcvi 

1.  Terms  derived  from  Latin  and  Greek               .  xcvi' 

2.  German  Terms       .....  xcvii 

3.  Descriptive  Terms      ....  c 

4.  Nomenclature.     Zoology                 .             .             .  c 

5. • Mineralogy   ...  cii 

6. Botany     .  .  .  .cii 

7. Chemistry     ...  cii 

8. Crystallography                 .             .  ciii 

Aphorism  XVI.,  relative  to  the  composition  and  inflexion 

of  Terms                  .....  cv 

1.  Hybrids          .             .             .             .  cvi 

2.  Terminations  of  Adjectives             .             .             .  cvii 

3.  Formation  of  Substantives  (names  of  things)  .  cviii 

4.  Abstract  Substantives        ....  cxiii 

5.  Rules  of  derivation  from  Greek  and  Latin      .  cxiv 

6.  Modifications  of  Terminations         .             .             .  cxv 
Aphorism   XVII.,   relative   to  the  mode  of  introducing 

Changes        .....  cxvii 


VI  CONTENTS. 

THE  PHILOSOPHY  OF  THE  INDUCTIVE  SCIENCES. 

PART  I.— OF  IDEAS. 
BOOK  I. — OF  IDEAS  IN  GENERAL. 

Page 

CHAP.  1.  INTRODUCTION              .            .             .             .  .3 

2.  Of  Facts  and  Theories           ....  18 

3.  Of  Sensations  and  Ideas           .             .             .  .25 

4.  Of  the  Difference  and  Opposition  of  Sensation  and  Ideas      28 

5.  Of  Ideal  Conceptions                .             .             .  .36 

6.  Of  Induction            .....  41 

7.  Of  Successive  Generalizations                .             .  .45 

8.  Of  Technical  Terms               .             .  50 

9.  Of  Necessary  and  Contingent  Truths                .  .       53 

10.  Of  Experience  .....  59 

11.  Of  the  Grounds  of  Necessary  Truths  .  .       63 

12.  The  Fundamental  Ideas  are  not  derived  from  Experience      71 

13.  Of  the  Philosophy  of  the  Sciences        .  .  -75 

BOOK  II. — THE  PHILOSOPHY  OF  THE  PURE  SCIENCES. 

CHAP.  1.  Of  the  Pure  Sciences            .             .             .  .           79 

2.  Of  the  Idea  of  Space  .             .             .             .  .81 

3.  Of  some  Peculiarities  of  the  Idea  of  Space  .  ..           85 

4.  Of  the  Definitions  and  Axioms  which  relate  to  Space         88 

5.  Of  some  Objections  to  the  Previous  Doctrines  .       98 

6.  Of  the  Perception  of  Space                .             .  .108 
*  6.  Of  the  Idea  of  Time                  .             .             .  .121 

7.  Of  some  Peculiarities  of  the  Idea  of  Time  .         124 

8.  Of  the  Axioms  which  relate  to  Number            .  .128 

9.  Of  the  Perception  of  Time  and  Number  .         131 

10.  Of  Mathematical  Reasoning     .  .  .  .135 

11.  Of  the  Foundations  of  the  Higher  Mathematics       .         139 

12.  Of  the  Doctrine  of  Motion        ....     144 

13.  Of  the  Application  of  Mathematics  to  the  Inductive 

Sciences  .  .  .  .  .147 

BOOK  III. — THE  PHILOSOPHY  OF  THE  MECHANICAL  SCIENCES. 

CHAP.  1.  Of  the  Mechanical  Sciences     .  .  .  .157 

2.  Of  the  Idea  of  Cause  .  .  .         ]59 

3.  Modern  Opinions  respecting  the  Idea  of  Cause  .     ]  63 

*  The  number  repeated  by  mistake. 


CONTENTS.  Vii 

Page 

4.  Of  the  Axioms  which  relate  to  the  Idea  of  Cause    .  169 

5.  Of  the  Origin  of  our  Conceptions  of  Force  and  Matter  177 

6.  Of  the  Establishment  of  the  Principles  of  Statics          .  184 

7.  Of  the  Establishment  of  the  Principles  of  Dynamics  207 

8.  Of  the  Paradox  of  Universal  Propositions  established 

by  Experience  ....         237 

9.  Of  the  Establishment  of  the  Law  of  Universal  Gravi- 

tation      ...  .  .  .246 

]0.  Of  the  General  Diffusion  of  Clear  Mechanical  Ideas         253 


BOOK  IV.  —  THE  PHILOSOPHY  OF  THE  SECONDARY  MECHANICAL 
SCIENCES. 

CHAP.  1.  Of  the  Idea  of  a  Medium  as  commonly  employed        .     267 

2.  Of  Peculiarities  in  the  Perceptions  of  the  Different 

Senses     ......         275 

3.  Successive  Attempts  at  the  Application  of  the  Idea  of 

a  Medium          .....         295 

4.  Of  the  Measure  of  Secondary  Qualities  .  .     306 

BOOK  V.  —  THE  PHILOSOPHY  OF  THE  MECHANICO-CHEMICAL  SCIENCES. 

CHAP.  1  .  Attempts  at  the  Scientific  Application  of  the  Idea  of 

Polarity  .....         331 

2.  Of  the  Connexion  of  Polarities  .  .  343 

BOOK  VI.  —  THE  PHILOSOPHY  OF  CHEMISTRY. 

CHAP.  1.  Attempts  to  conceive  Elementary  Composition  .    361 

2.  Establishment  and  Development  of  the  Idea  of  Che- 

mical Affinity  .  .  .         373 

3.  Of  the  Idea  of  Substance          .  .  .  .    388 

4.  Application  of  the  Idea  of  Substance  in  Chemistry  396 

5.  The  Atomic  Theory  .  .  .405 

BOOK  VII.  —  THE  PHILOSOPHY  OF  MORPHOLOGY,  INCLUDING 
CRYSTALLOGRAPHY. 

CHAP.  1.  Explication  of  the  Idea  of  Symmetry  .  .         423 

2.  Application  of  the  Idea  of  Symmetry  to  Crystals         .     431 

3.  Speculations  founded  upon  the  Symmetry  of  Crystals       436 


Vlll  CONTENTS. 


BOOK  VIII. — PHILOSOPHY  OF  THE  CLASSIFICATORY  SCIENCES. 

Page 

CHAP.  1 .  Of  the  Idea  of  Likeness  as  governing  the  use  of  Com- 
mon Names          .....     449 

2.  Of  the  Methods  of  Natural  History  as  regulated  by  the 

Idea  of  Likeness  ....     462 

3.  Application  of  the  Natural  History  Method  to  Mine- 

ralogy     .  .  .  .  .  494 

4.  Of  the  Idea  of  Natural  Affinity        .  .  .510 


PREFACE. 


THE  Work  now  before  the  Reader  is  intended  as  an 
application  of  the  Plan  of  Bacon's  Novum  Organum  to 
the  present  condition  of  Physical  Science.  The  progress 
of  such  Science  during  the  last  three  centuries  has  given 
us  the  means  of  inquiring,  with  advantages  which  former 
generations  did  not  possess,  what  that  Organ,  or  intellec- 
tual method,  is,  by  which  solid  truth  is  to  be  extracted 
from  the  observation  of  Nature ;  and  though  the  attempt 
to  discover  this  cannot  but  be  an  arduous  undertaking,  it 
is  so  plainly  required  of  the  present  generation,  that  any 
one  engaging  in  it  with  sobriety  and  industry,  may  claim 
to  have  his  labours  soberly  and  tolerantly  estimated.  I 
shall,  therefore,  make  no  apology  for  what  might  otherwise 
appear  the  presumption  of  such  a  design.  My  scheme  is, 
however,  narrower  than  Bacon's  in  this  respect,  that  I 
have  in  the  present  work  confined  myself  to  those 
branches  of  human  knowledge  which  have  external 
nature  for  their  object,  and  are  often  exclusively  termed 
Sciences.  The  reason  given  for  this  limitation  in  the 
following  pages,  (namely,  that  it  seemed  proper  to  collect 
our  philosophy  of  knowledge  from  the  most  certain  and 
distinct  portions  of  knowledge  alone,)  will,  I  trust,  be 
considered  as  an  adequate  justification  of  the  course 
pursued. 

VOL.  i.  b 


X  PREFACE. 

Many  writers,   both   before   and    since  Bacon,   have 
employed  themselves  upon  the   subjects  with  which  we 
are  here  concerned ; — the  philosophy  of  knowledge,  and 
the  methods  of  arriving  at  science :    and  I  have  availed 
myself  of  their  conclusions,  where  they  appeared  to  be  real 
additions  to  sound  philosophy.     I  must  add,  that  I  have 
not  scrupled  to  subject  their  speculations  to   a  critical 
examination,  and  to  reject  all  that  was  thus  found  to  be 
erroneous  or  worthless.    A  system  which  professes  to  give 
a  view  of   the  nature   of  knowledge,  supplies  canons  of 
criticism  by  which  all  other  philosophical  doctrines  must 
be  tried,  in  order  to  determine  their  import  and  reality. 
It  is  an  office  essentially  connected  with  the  exposition  of 
such  a  system,  to  pronounce  on  the  value  of  previous 
essays  of  the  same  kind.     Hence  I  have  not  hesitated, 
on  some  occasions,  to  dissent  from  the  great  masters  of 
the  philosophy  of  science,  from  Bacon,  from  Cuvier,  and 
even  from  Newton  himself;   believing  that  they,  upon 
maturer  consideration,  would  have  been  led  to  those  doc- 
trines and  precepts  which  I  have  preferred  to  theirs.     In 
like  manner,  although  I  have  adopted  Kant's  reasoning 
respecting  the  nature  of  Space  and  Time,  it  will  be  found 
by  any   one   acquainted  with   the  system  of  that  acute 
metaphysician,  that  my  views  differ  widely  from  his.     I 
have    also  ventured  to   condemn  some   of  the   opinions 
respecting  physical  philosophy,  published  by  another  emi- 
nent German  writer  (Schelling)  to  whose  works  I  have  in 
other  subjects  great  obligations. 

The  present  work  was  announced  in  the  outset  of  a 


PREFACE  Xi 

History  of  the  Inductive  Sciences  which  was  published  three 
years  ago.  That  History  was,  indeed,  the  result  of  labours 
undertaken  with  a  view  to  the  formation  of  a  PJiilosophy 
of  Science,  and  was  intended  from  the  first  as  an  intro- 
duction to  a  work  on  that  subject.  I  may  therefore  take 
the  liberty  of  saying*  that  I  have  as  yet  seen  no  reason  to 
wish  to  make  any  material  change  in  the  History,  as  it  is 
now  before  the  world.  I  will  not  omit  this  opportunity 
of  expressing  my  obligations  to  the  German  translator  of 
the  History*.  It  is  a  testimony  which  may  well  give  an 
author  some  confidence  in  the  value  of  his  work,  that 
one  of  the  most  eminent  men  of  science  in  Europe  should 
spontaneously  postpone  other  tasks  in  order  to  give  it, 
with  the  most  flattering  expressions,  to  the  public  of  his 
own  country.  I  may  add  that  a  Review  of  my  History 
which  has  appeared  in  our  own  language  has  tended  in 
no  small  degree  to  convince  me  that  the  work  contains 
few  material  errors,  and  none  which  are  of  any  importance 
with  regard  to  its  general  scope.  The  Reviewer,  ob- 
viously an  enemy  eager  to  find  faults,  was  able  to  detect 
but  very  few  passages  which  are  really  mistakes  f. 

Other  critics  have  made  objections  of  various  kinds  to 

*  The  History  of  the  Inductive  /Sciences  has  been  translated  into 
German  by  M.  Yon  Littrow,  Director  of  tlie  Imperial  Observatory  at 
Vienna,  and  author  of  many  well-known  mathematical  works. 

t  See  Edinburgh  Review,  No.  cxxxiii.  p.  129  ;  also  No.  cxxxvi.,  p. 
274.  But  I  am  compelled  by  justice  to  acknowledge  that  the  value  of 
this  testimony  is  materially  weakened  by  the  Reviewer's  extreme  laxity 
and  obscurity  of  view  with  regard  to  the  nature  of  science ; — defects 
which  make  his  judgment  on  such  subjects  nearly  worthless. 

b  2 


Xll  PREFACE. 

that  part  of  the  History  which  relates  to  Physiology ;  but 
none  which  it  is  necessary  to  notice  here.  I  regret  that 
my  plan  should  again  lead  me,  in  the  present  work,  to 
trespass  upon  the  domain  of  the  physiologists.  Those  who 
have  well  studied  that  subject,  feel  a  persuasion,  a  very 
natural  and  just  one,  that  nothing  less  than  a  life  profes- 
sionally devoted  to  the  science,  can  entitle  a  person  to 
decide  the  still  controverted  questions  which  it  involves ; 
and  hence  they  look,  with  a  reasonable  jealousy,  upon 
attempts  to  discuss  such  questions,  made  by  a  lay  specu- 
lator. I  trust  it  will  be  found  that  I  have  not,  in  the 
present  work,  asserted  any  opinions  on  such  subjects,  with- 
out alleging  sufficient  reasons.  Such  discussions  as  I 
have  introduced,  appeared  to  me  to  be  requisite  to  com- 
plete the  philosophy  of  science  :  the  value  of  the  opinions 
thus  delivered,  it  must  be  left  to  physiologists,  present 
and  future,  to  decide. 

In  writing  the  History,  I  was  led,  on  several  occasions, 
to  pass  on  from  the  facts  to  the  lessons  of  philosophy  which 
they  suggest.  I  have  now,  in  three  or  four  instances, 
taken  the  liberty  of  restoring  reflections  so  made  to  their 
proper  place,  by  incorporating  a  few  phrases,  or  here 
and  there  a  sentence,  from  the  History,  in  the  present 
work.  I  think  it  right  to  mention  this,  that  those  who 
read  both  works  may  not  deem  me  guilty  of  careless 
repetition. 

Perhaps  I  shall  be  charged  with  having  employed  the 
term  Idea  in  an  unusual  manner  in  these  pages.  Almost 
every  writer  who  has  introduced  that  term  into  his  spe- 


PREFACE.  Xiii 

dilations,  has  been  accused,  by  succeeding  critics,  of 
some  degree  of  vagueness  and  vacillation  in  its  use.  The 
mode  in  which  I  have  applied  it  appears  to  me  very  defi- 
nite. The  grounds  of  the  universal  and  necessary  truths 
which  we  are  able  to  assert  in  various  departments  of 
knowledge,  reside  in  certain  general  forms  of  apprehen- 
sion, or  relations  of  our  conceptions;  as  Space,  Time, 
Cause ;  and  these  I  term  Ideas ;  or,  when  ambiguity  is  to 
be  guarded  against,  Fundamental  Ideas.  If  I  could  have 
found  any  other  word  or  phrase  which,  in  common  usage, 
came  nearer  to  this  meaning,  I  should  have  been  glad  to 
adopt  it.  I  have  employed  the  word  Conception  to  ex- 
press that  which  is,  I  think,  its  common  signification ; — 
our  Conceptions  are  that,  in  the  mind,  which  we  denote  by 
our  General  Terms,  as  a  Triangle,  a  Square  Number, 
a  Force.  But  still,  this  term,  in  the  present  work,  implies 
principles  which  have  not  been  employed,  at  least  not 
commonly,  by  previous  writers.  For  in  the  course  of  my 
speculations,  I  am  further  led  to  speak  of  such  Concep- 
tions as  Modifications  of  our  Fundamental  Ideas ;  and  as 
deriving  from  the  Ideas  their  power  of  leading  to  uni- 
versal and  necessary  truths.  In  instances  in  which  no 
obscurity  appeared  likely  to  arise,  I  may,  perhaps,  occa- 
sionally have  employed  the  terms  Idea,  Conception, 
Notion,  and  others,  with  less  discrimination. 

Bacon's  purpose  and  promise  was,  that  his  New  Organ 
should  produce  material  as  well  as  intellectual  profit ; — 
works,  as  well  as  knowledge.  That  the  study  of  the 
order  of  nature  does  add  to  man's  power,  the  history  of 


XIV  PREFACE. 

the   sciences  since  Bacon  has  abundantly  shown.     But 
though  this  hope  of  derivative  advantages  may  stimulate 
our  exertions,  it  cannot  govern    our  methods  of  seeking 
knowledge,  without  leading  us  away  from  the  most  gene- 
ral and   genuine    forms   of  knowledge.     The   nature   of 
knowledge  must  be  studied  in  itself  and  for  its  own  sake, 
before  we  attempt  to  learn  what  external  rewards  it  will 
bring  us.     I  have,  therefore,  not  aimed  at  imitating  Bacon 
in  those  parts  of  his  work,  in  which  he  contemplates  the 
increase  of  man's  dominion    over  nature,    as   the  main 
object  of  natural  philosophy ;  being  fully  persuaded    that 
if  Bacon  himself  had  had  unfolded  before  him  the  great 
theories  which  have  been  established  since  his  time,  he 
would  have  acquiesced   in  the  contemplation   of  them ; 
and  would  have  readily  proclaimed  the  real  reason  for 
aiming  at  the  knowledge  of  such  truths  to  be,  that  they 
are  true.     Thus  I  have  ventured   to   separate   his   first 
Aphorism*  into  two ;  to  consider  the  Interpretation  as  our 
primary  object,  not  the  ministration;  tlie knowing,  not  the 
doing ;  the  Intelligence,  not  the  Power. 

The  mode  of  delivering  the  philosophy  of  science  in 
Aphorisms  which  Bacon  has  adopted,  would  not  well  suf- 
fice for  the  treatment  of  the  subject  at  present,  since 
many  questions  must  be  discussed,  many  perplexities  ex- 
plained. No  writer  upon  such  subjects  can  expect  to  be 
either  understood  or  assented  to,  beyond  the  limits  of  a 

*  Homo  naturae  minister  et  interpres  tantum  facit  et  intelligit 
quantum  de  naturae  ordine  re  vel  mente  observaverit;  nee  amplius  scit 
aut  potest. 


PREFACE.  XV 

narrow  school,  who  is  not  prepared  with  good  arguments, 
as  wrell  as  magisterial  decisions,  upon  the  many  obscure 
and  controverted  points  which  the  subject  brings  before 
him.  But  though  an  Aphoristic  Philosophy,  unsupported 
by  reasoning,  is  thus  unsuited  to  the  time,  it  may  be  satis- 
factory to  many  readers  to  see  the  Philosophy  to  which  in 
the  present  work  we  are  led,  presented  in  the  Aphoristic 
form.  I  have,  therefore,  expressed  in  Aphorisms  a  large 
part  of  the  doctrines  resulting  from  the  discussions  which 
occupy  the  following  pages.  These  Aphorisms  are  given 
at  the  end  of  this  Preface. 

Along  with  these,  I  shall  add  some  other  Aphorisms 
on  the  subject  of  the  Language  of  Science ;  a  subject  in 
which  it  appears  to  be  time  to  collect,  from  the  usage  of 
the  most  judicious  writers,  some  rules  which  may  tend  to 
preserve  the  purity  and  analogies  of  scientific  language 
from  wanton  and  needless  violation.  As  this  subject  is 
not  discussed  in  the  work  itself,  I  have  given,  along  with 
these  Aphorisms,  such  examples  as  may  tend  to  confirm 
and  illustrate  them,  and  have  applied  them  to  some  cases 
at  present  unsettled. 


APHORISMS  CONCERNING  IDEAS. 


I. 

MAN  is  the  Interpreter  of  Nature,  Science  the  right  interpre- 
tation. 

II. 

The  Senses  place  before  us  the  Characters  of  the  Book  of 
Nature ;  but  these  convey  no  knowledge  to  us,  till  we  have  dis- 
covered the  Alphabet  by  which  they  are  to  be  read. 

III. 

The  Alphabet,  by  means  of  which  we  interpret  Phenomena, 
consists  of  the  Ideas  existing  in  our  own  minds;  for  these  give  to 
the  phenomena  that  coherence  and  significance  which  is  not  an 
object  of  sense. 

IV. 

The  antithesis  of  Sense  and  Ideas  is  the  foundation  of  the 
Philosophy  of  Science.  No  knowledge  can  exist  without  the 
union,  no  philosophy  without  the  separation,  of  these  two  ele- 
ments. 

V. 

Fact  and  Theory  correspond  to  Sense  on  the  one  hand,  and  to 
Ideas  on  the  other,  so  far  as  we  are  conscious  of  our  Ideas :  but 
all  facts  involve  ideas  unconsciously ;  and  thus  the  distinction  of 
Facts  and  Theories  is  not  tenable,  as  that  of  Sense  and  Ideas  is. 

VI. 

Sensations  and  Ideas  in  our  knowledge  are  like  Matter  and 
Form  in  bodies.  Matter  cannot  exist  without  Form,  nor  Form 


XV111  APHORISMS 

without  Matter  :  yet  the  two  are  altogether  distinct  and  opposite. 
There  is  no  possibility  either  of  separating,  or  of  confounding 
them.  The  same  is  the  case  with  Sensations  and  Ideas. 

VII. 

Ideas  are  not  transformed,  but  ^formed  Sensations ;  for  with- 
out ideas,  sensations  have  no  form. 

VIII. 

The  Sensations  are  the  Objective,  the  Ideas  the  Subjective  part 
of  every  act  of  perception  or  knowledge. 

IX. 

General  terms  denote  Ideal  Conceptions,  as  a  circle,  an  orbit, 
a  rose.  These  are  not  images  of  real  things,  as  was  held  by  the 
Realists,  but  conceptions :  yet  they  are  conceptions,  not  bound 
together  by  mere  name,  as  the  Nominalists  held,  but  by  an  idea. 

X. 

It  has  been  said  by  some,  that  all  Conceptions  are  merely 
states  or  feelings  of  the  mind,  but  this  assertion  only  tends  to  con- 
found what  it  is  our  business  to  distinguish. 

XI. 

Observed  Facts  are  connected  so  as  to  produce  new  truths,  by 
superinducing  upon  them  an  Idea :  and  such  truths  are  obtained 
by  Induction. 

XII. 

Truths  once  obtained  by  legitimate  Induction  are  Facts : 
these  Facts  may  be  again  connected,  so  as  to  produce  higher  truths : 
and  thus  we  advance  to  Successive  Generalizations. 

XIII. 

Truths  obtained  by  Induction  are  made  compact  and  perma- 
nent by  being  expressed  in  Technical  Terms. 


CONCERNING    IDEAS. 


XIV. 

Experience  cannot  conduct  us  to  universal  and  necessary 
truths  :  —  Not  to  universal,  because  she  has  not  tried  all  cases  :  — 
Not  to  necessary,  because  necessity  is  not  a  matter  to  which  expe- 
rience can  testify. 

XV. 

Necessary  truths  derive  their  necessity  from  the  Ideas  which 
they  involve  ;  and  the  existence  of  necessary  truths  proves  the 
existence  of  Ideas  not  generated  by  experience. 

XVI. 

In  Deductive  Reasoning,  we  cannot  have  any  truth  in  the 
conclusion  which  is  not  virtually  contained  in  the  premises. 

XVII. 

In  order  to  acquire  any  exact  and  solid  knowledge,  the  student 
must  possess  with  perfect  precision  the  ideas  appropriate  to  that 
part  of  knowledge  :  and  this  precision  is  tested  by  the  student's 
perceiving  the  axiomatic  evidence  of  the  axioms  belonging  to  each 
Fundamental  Idea. 

XVIII. 

The  Fundamental  Ideas  which  it  is  most  important  to  con- 
sider, as  being  the  Bases  of  the  Material  Sciences,  are  the  Ideas 
of  Space,  Time  (including  Number),  Cause  (including  Force  and 
Matter),  Outness  of  Objects,  and  Media  of  Perception  of  Secondary 
Qualities,  Polarity  (Contrariety),  Chemical  Composition  and 
Affinity,  Substance,  Likeness  and  Natural  Affinity,  Means  and 
Ends  (whence  the  notion  of  Organization),  Symmetry,  and  the 
Ideas  of  Vital  Poicers. 

XIX. 

The  Sciences  which  depend  upon  the  Ideas  of  Space  and 
Number  are  Pure  Sciences,  not  Inductive  Sciences  :  they  do  not 
infer  special  Theories  from  Facts,  but  deduce  the  conditions  of  all 
theory  from  Ideas.  The  Elementary  Pure  Sciences,  or  Elemen- 
tary Mathematics,  are  Geometry,  Theoretical  Arithmetic  and 
Algebra. 


XX  APHORISMS 


XX. 

The  Ideas  on  which  the  Pure  Sciences  depend,  are  those  of 
Space  and  Number ;  but  Number  is  a  modification  of  the  concep- 
tion of  Repetition,  which  belongs  to  the  Idea  of  Time. 

XXI. 

The  Idea  of  Space  is  not  derived  from  experience,  for  expe- 
rience of  external  objects  presupposes  bodies  to  exist  in  Space. 
Space  is  a  condition  under  which  the  mind  receives  the  impres- 
sions of  sense,  and  therefore  the  relations  of  space  are  necessarily 
and  universally  true  of  all  perceived  objects.  Space  is  a  form  of 
our  perceptions,  and  regulates  them,  whatever  the  matter  of  them 
may  be. 

XXII. 

Space  is  not  a  general  notion  collected  by  abstraction  from 
particular  cases ;  for  we  do  not  speak  of  Spaces  in  general,  but  of 
universal  or  absolute  Space.  Absolute  space  is  infinite.  All 
special  spaces  are  in  absolute  space,  and  are  parts  of  it. 

XXIII. 

Space  is  not  a  real  object  or  thing,  distinct  from  the  objects 
which  exist  in  it ;  but  it  is  a  real  condition  of  the  existence  of 
external  objects. 

XXIV. 

We  have  an  Intuition  of  objects  in  space ;  that  is,  we  con- 
template objects  as  made  up  of  spatial  parts,  and  apprehend  their 
spatial  relations  by  the  same  act  by  which  we  apprehend  the 
objects  themselves. 

XXV. 

Form  or  figure  is  space  limited  by  boundaries.  Space  has 
necessarily  three  dimensions,  length,  breadth,  depth;  and  no 
ethers  which  cannot  be  resolved  into  these. 


CONCERNING   IDEAS,  Xxi 


XXVI. 

The  Idea  of  Space  is  exhibited  for  scientific  purposes,  by  the 
Definitions  and  Axioms  of  Geometry ;  such,  for  instance,  as 
these : — the  Definition  of  a  Right  Angle,  and  of  a  Circle ; — the 
Definition  of  Parallel  Lines,  and  the  Axiom  concerning  them; — 
the  Axiom  that  two  straight  lines  cannot  inclose  a  space.  These 
Definitions  are  necessary,  not  arbitrary;  and  the  Axioms  are 
needed  as  well  as  the  Definitions,  in  order  to  express  the  neces- 
sary conditions  which  the  Idea  of  Space  imposes. 

XXVII. 

The  Definitions  and  Axioms  of  Elementary  Geometry  do  not 
completely  exhibit  the  Idea  of  Space.  In  proceeding  to  the 
Higher  Geometry,  we  may  introduce  other  additional  and  inde- 
pendent Axioms ;  such  as  that  of  Archimedes,  that  a  curve  line 
u'hich  joins  tic  o  points  is  less  than  any  broken  line  joining  the  same 
points  and  including  the  curve  line. 

XXVIII. 

The  perception  of  a  solid  object  by  sight  requires  that  act  of 
mind  by  which,  from  figure  and  shade,  we  infer  distance  and 
position  in  space.  The  perception  of figure  by  sight  requires  that 
act  of  mind  by  which  we  give  an  outline  to  each  object. 

XXIX. 

The  perception  of  form  by  touch  is  not  an  impression  on  the 
passive  sense,  but  requires  an  act  of  our  muscular  frame  by  which 
we  become  aware  of  the  position  of  our  own  limbs.  The  percep- 
tive faculty  involved  in  this  act  has  been  called  the  muscular  sense. 

XXX. 

The  Idea  of  Time  is  not  derived  from  experience,  for  expe- 
rience of  changes  jo/vsupposes  occurrences  to  take  place  in  Time. 
Time  is  a  condition  under  which  the  mind  receives  the  impres- 
sions of  sense,  and  therefore  the  relations  of  tin\e  are  necessarily 


XXH  APHORISMS 

and  universally  true  of  all  perceived  occurrences.  Time  is  a.  form 
of  our  perceptions,  and  regulates  them,  whatever  the  matter  of 
them  may  be. 

XXXI. 

Time  is  not  a  general  notion  collected  by  abstraction  from 
particular  cases.  For  we  do  not  speak  of  particular  Times  as 
examples  of  time  in  general,  but  as  parts  of  a  single  and  infinite 
Time. 

XXXII. 

Time,  like  Space,  is  a  form,  not  only  of  perception,  but  of 
Intuition.  We  consider  the  whole  of  any  time  as  equal  to  the 
sum  of  the  parts  ;  and  an  occurrence  as  coinciding  with  the  por- 
tion of  time  which  it  occupies. 

XXXIII. 

Time  is  analogous  to  Space  of  one  dimension:  portions  of 
both  have  a  beginning  and  an  end,  are  long  or  short.  There  is 
nothing  in  Time  which  is  analogous  to  Space  of  two,  or  of  three, 
dimensions,  and  thus  nothing  which  corresponds  to  Figure. 

XXXIV. 

The  Repetition  of  a  set  of  occurrences,  as,  for  example,  strong 
and  weak,  or  long  and  short  sounds,  according  to  a  steadfast  order, 
produces  Rhythm,  which  is  a  conception  peculiar  to  Time,  as 
Figure  is  to  Space. 

XXXV. 

The  simplest  form  of  Repetition  is  that  in  which  there  is  no 
variety,  and  this  gives  rise  to  the  conception  of  Number. 

XXXVI. 

The  simplest  numerical  truths  are  seen  by  Intuition  ;  when 
we  endeavour  to  deduce  the  more  complex  from  these  simplest, 
we  employ  such  maxims  as  these  : — If  equals  be  added  to  equah 
the  wholes  are  equal: — If  equals  be  subtracted  from  equals  the 
remainders  are  equal: — The  whole  is  equal  to  the  sum  of  all  its  parts. 


CONCERNING    IDEAS.  XXili 


XXXVII. 

The  Perception  of  Time  involves  a  constant  and  latent  kind 
of  memory,  which  may  be  termed  a  Sense  of  Succession.  The 
Perception  of  Number  also  involves  this  Sense  of  Succession, 
although  in  small  numbers  we  appear  to  apprehend  the  units 
simultaneously  and  not  successively. 

XXXVIII. 

The  Perception  of  Rhythm  is  not  an  impression  on  the  pas- 
sive sense,  but  requires  an  act  of  thought  by  which  we  connect 
and  group  the  strokes  which  form  the  Rhythm. 

XXXIX. 

Intuitive  is  opposed  to  discursive  reason.  In  intuition,  we 
obtain  our  conclusions  by  dwelling  upon  one  aspect  of  the  funda- 
mental Idea  ;  in  discursive  reasoning,  we  combine  several  aspects 
of  the  Idea,  (that  is,  several  axioms,)  and  reason  from  the  combi- 
nation. 

XL. 

Geometrical  deduction  (and  deduction  in  general)  is  called 
synthesis,  because  we  introduce,  at  successive  steps,  the  results  of 
new  principles.  But  in  reasoning  on  the  relations  of  space,  we 
sometimes  go  on  separating  truths  into  their  component  truths, 
and  these  into  other  component  truths ;  and  so  on ;  and  this  is 
geometrical  analysis. 

XLI. 

Among  the  foundations  of  the  Higher  Mathematics,  is  the 
Idea  of  Symbols  considered  as  general  Signs  of  Quantity.  This 
idea  of  a  Sign  is  distinct  from,  and  independent  of  other  ideas. 
The  axiom  to  which  we  refer  in  reasoning  by  means  of  Symbols 
of  quantity  is  this  : — The  interpretation  of  such  symbols  must  be 
perfectly  general.  This  Idea  and  Axiom  are  the  bases  of  Algebra 
in  its  most  general  form. 


XXIV  APHORISMS 

XLII. 

Among  the  foundations  of  the  Higher  Mathematics  is  also 
the  Idea  of  a  Limit.  The  Idea  of  a  Limit  cannot  be  superseded 
by  any  other  definitions  or  Hypotheses.  The  Axiom  which  we 
employ  in  introducing  this  Idea  into  our  reasoning  is  this: — 
What  is  true  up  to  the  Limit  is  true  at  the  Limit.  This  Idea  and 
Axiom  are  the  bases  of  all  Methods  of  Limits,  Fluxions,  Diffe- 
rentials, Variations,  and  the  like. 

XLIII. 

There  is  a  pure  Science  of  Motion,  which  does  not  depend 
upon  observed  facts,  but  upon  the  Idea  of  motion.  It  may 
also  be  termed  Pure  Mechanism,  in  opposition  to  Mechanics 
Proper,  or  Machinery,  which  involves  the  mechanical  conceptions 
of  force  and  matter.  It  has  been  proposed  to  name  this  Pure 
Science  of  Motion,  Kinematics. 

XLIV. 

The  pure  mathematical  sciences  must  be  successfully  culti- 
vated, in  order  that  the  progress  of  the  principal  inductive  sciences 
may  take  place.  This  appears  in  the  case  of  Astronomy,  in 
which  Science,  both  in  ancient  and  in  modern  times,  each  advance 
of  the  theory  has  depended  upon  the  previous  solution  of  problems 
in  pure  mathematics.  It  appears  also  inversely  in  the  Science  of 
the  Tides,  in  which,  at  present,  we  cannot  advance  in  the  theory, 
because  we  cannot  solve  the  requisite  problems  in  the  Integral 
Calculus. 

XLV. 

The  Idea  of  Cause,  modified  into  the  conceptions  of  mecha- 
nical cause,  or  Force,  and  resistance  to  force,  or  Matter,  is  the 
foundation  of  the  Mechanical  Sciences ;  that  is,  Mechanics, 
(including  Statics  and  Dynamics,)  Hydrostatics,  and  Physical 
Astronomy. 

XLVI. 

The  Idea  of  Cause  is  not  derived  from  experience ;  for  in 
judging  of  occurrences  which  we  contemplate,  we  consider  them 


CONCERNING  IDEAS.  XXV 

as  being,  universally  and  necessarily,  Causes  and  Effects,  which 
a  finite  experience  could  not  authorize  us  to  do.  The  Axiom, 
that  every  event  must  have  a  cause,  is  true  independently  of 
experience,  and  beyond  the  limits  of  experience. 

XLVII. 

The  Idea  of  Cause  is  expressed  for  purposes  of  science  by 
these  three  Axioms : — Every  Event  must  have  a  Cause : — Causes 
are  measured  by  their  Effects : — Reaction  is  equal  and  opposite  to 
Action. 

XLVIIT. 

The  Conception  of  Force  involves  the  Idea  of  Cause,  as  applied 
to  the  motion  and  rest  of  bodies.  The  conception  of  force  is 
suggested  by  muscular  action  exerted :  the  conception  of  matter 
arises  from  muscular  action  resisted.  We  necessarily  ascribe  to 
all  bodies  solidity  and  inertia,  since  we  conceive  Matter  as  that 
which  cannot  be  compressed  or  moved  without  resistance. 

XLIX. 

Mechanical  Science  depends  on  the  Conception  of  Force ; 
and  is  divided  into  Statics,  the  doctrine  of  Force  preventing 
motion,  and  Dynamics,  the  doctrine  of  Force  producing  motion. 

L. 

The  Science  of  Statics  depends  upon  the  Axiom,  that  Action 
and  Reaction  are  equal,  which  in  Statics  assumes  this  form : 
—  When  two  equal  weights  are  supported  on  the  middle  point 
between  them,  the  pressure  on  the  fulcrum  is  equal  to  the  sum  of  the 
weights. 

LI. 

The  Science  of  Hydrostatics  depends  upon  the  Fundamental 
Principle  that  fluids  press  equally  in  all  directions.  This  Prin- 
ciple necessarily  results  from  the  conception  of  a  Fluid,  as  a  body 
of  which  the  parts  are  perfectly  moveable  in  all  directions.  For 
since  the  Fluid  is  a  body,  it  can  transmit  pressure ;  and  the  trans- 
mitted pressure  is  equal  to  the  original  pressure,  in  virtue  of  the 
VOL.  I.  c 


XXVi  APHORISMS 

Axiom  that  Reaction  is  equal  to  Action.  That  the  Fundamental 
Principle  is  not  derived  from  experience,  is  plain  both  from  its 
evidence  and  from  its  history. 

LII. 

The  Science  of  Dynamics  depends  upon  the  three  Axioms 
above  stated  respecting  Cause.  The  First  Axiom, — that  every 
change  must  have  a  Cause, — gives  rise  to  the  First  Law  of 
Motion, — that  a  body  not  acted  upon  by  a  force  will  move  with  a 
uniform  velocity  in  a  straight  line.  The  Second  Axiom, — that 
Causes  are  measured  by  their  Effects, — gives  rise  to  the  Second 
Law  of  Motion, — that  when  a  force  acts  upon  a  body  in  motion, 
the  effect  of  the  force  is  compounded  with  the  previously  existing 
motion.  The  Third  Axiom, — that  Reaction  is  equal  and  opposite 
to  Action, — gives  rise  to  the  Third  Law  of  Motion,  which  is 
expressed  in  the  same  terms  as  the  Axiom ;  Action  and  Reaction 
being  understood  to  signify  momentum  gained  and  lost. 

LIII. 

The  above  Laws  of  Motion,  historically  speaking,  were  esta- 
blished by  means  of  experiment :  but  since  they  have  been  dis- 
covered and  reduced  to  their  simplest  form,  they  have  been  con- 
sidered by  many  philosophers  as  self-evident.  This  result  is 
principally  due  to  the  introduction  and  establishment  of  terms 
and  definitions,  which  enable  us  to  express  the  Laws  in  a  very 
simple  manner. 

LIV. 

In  the  establishment  of  the  Laws  of  Motion,  it  happened,  in 
several  instances,  that  Principles  were  assumed  as  self-evident 
which  do  not  now  appear  evident,  but  which  have  since  been  de- 
monstrated from  the  simplest  and  most  evident  principles.  Thus 
it  was  assumed  that  a  perpetual  motion  is  impossible ; — that  the 
velocities  of  bodies  acquired  by  falling  down  planes  or  curves  of  the 
same  vertical  height  are  equal ; — that  the  actual  descent  of  the 
centre  of  gravity  is  equal  to  its  potential  ascent.  But  we  are  not 
hence  to  suppose  that  these  assumptions  were  made  without 
ground :  for  since  they  really  follow  from  the  laws  of  motion, 


CONCERNING  IDEAS.  XXVll 

they  were  probably,  in  the  minds  of  the  discoverers,  the  results 
of  undeveloped  demonstrations  which  their  sagacity  led  them  to 
divine. 

LV. 

It  is  a  Paradox  that  Experience  should  lead  us  to  truths  con- 
fessedly universal,  and  apparently  necessary,  such  as  the  Laws  of 
Motion  are.  The  Solution  of  {his  paradox  is,  that  these  laws  are 
interpretations  of  the  Axioms  of  Causation.  The  Axioms  are 
universally  and  necessarily  true,  but  the  right  interpretation  of 
the  terms  which  they  involve,  is  learnt  by  experience.  Our 
Idea  of  Cause  supplies  the  Form,  Experience,  the  Matter,  of  these 
Laws. 

LVI. 

Primary  Qualities  of  Bodies  are  those  which  we  can  con- 
ceive as  directly  perceived  ;  Secondary  Qualities  are  those  which 
we  conceive  as  perceived  by  means  of  a  Medium. 

LVII. 

We  necessarily  perceive  bodies  as  without  us :  the  Idea  of 
Externality  is  one  of  the  conditions  of  perception. 

LVIII. 

We  necessarily  assume  a  Medium  for  the  perceptions  of  Light, 
Colour,  Sound,  Heat,  Odours,  Tastes ;  and  this  Medium  must 
convey  impressions  by  means  of  its  mechanical  attributes. 

LIX. 

Secondary  Qualities  are  not  extended  but  intensive ;  their 
effects  are  not  augmented  by  addition  of  parts,  but  by  increased 
operation  of  the  medium.  Hence  they  are  not  measured  directly, 
but  by  scales;  not  by  units,  but  by  degrees. 

LX. 

In  the  Scales  of  Secondary  Qualities,  it  is  a  condition  (in 
order  that  the  scale  may  be  complete,)  that  every  example  of  the 
quality  must  either  agree  with  one  of  the  degrees  of  the  Scale, 
or  lie  between  two  contiguous  degrees. 

c  2 


XXV111  APHORISMS 

LXI. 

We  perceive  by  means  of  a  medium  and  by  means  of  impres- 
sions on  the  nerves :  but  we  do  not  (by  our  senses,)  perceive 
either  the  medium  or  the  impressions  on  the  nerves. 

LXII. 

• 

The  Prerogatives  of  the  Sight  are,  that  by  this  sense  we  neces- 
sarily and  immediately  apprehend  the  position  of  its  objects :  and 
that  from  visible  circumstances,  we  infer  the  distance  of  objects 
from  us,  so  readily  that  we  seem  to  perceive  and  not  to  infer. 

LXIII. 

The  Prerogatives  of  the  Hearing  are,  that  by  this  sense  we 
perceive  relations  perfectly  precise  and  definite  between  two  notes, 
namely,  Musical  Intervals  (as  an  Octave,  a  Fifth) ;  and  that  when 
two  notes  are  perceived  together,  they  are  apprehended  as  dis- 
tinct, (a  Chord,)  and  as  having  a  certain  relation,  (Concord  or 
Discord.) 

LXIV. 

The  Sight  cannot  decompose  a  compound  colour  into  simple 
colours,  or  distinguish  a  compound  from  a  simple  colour.  The 
Hearing  cannot  directly  perceive  the  place,  still  less  the  distance, 
of  its  objects.  We  infer  these  obscurely  and  vaguely  from 
audible  circumstances. 

LXV. 

The  First  Paradox  of  Vision  is,  that  we  see  objects  upright, 
though  the  images  on  the  retina  are  inverted.  The  solution  is, 
that  we  do  not  see  the  image  on  the  retina  at  all,  we  only  see  by 
means  of  it. 

LXVL 

The  Second  Paradox  of  Vision  is,  that  we  see  objects  single, 
though  there  are  two  images  on  the  retinas,  one  in  each  eye. 
The  explanation  is,  that  it  is  a  Law  of  Vision  that  we  see  (small 
or  distant)  objects  single,  when  their  images  fall  on  corresponding 
points  of  the  two  retinas. 


CONCERNING    IDEAS.  XXIX 

LXVIL 

The  law  of  single  vision  for  near  objects  is  this  : — When  the 
two  images  in  the  two  eyes  are  situated,  part  for  part,  nearly  but 
not  exactly,  upon  corresponding  points,  the  object  is  apprehended 
as  single  and  solid  if  the  two  images  are  such  as  would  be  pro- 
duced by  a  single  solid  object  seen  by  the  eyes  separately. 

LXVIII. 

The  ultimate  object  of  each  of  the  Secondary  Mechanical 
Sciences  is,  to  determine  the  nature  and  laws  of  the  processes  by 
which  the  impression  of  the  Secondary  Quality  treated  of  is  con- 
veyed :  but  before  we  discover  the  cause,  it  may  be  necessary  to 
determine  the  laws  of  the  phenomena ;  and  for  this  purpose  a 
Measure  or  Scale  of  each  quality  is  necessary. 

LXIX. 

Secondary  qualities  are  measured  by  means  of  such  effects  as 
can  be  estimated  in  number  or  space. 

LXX. 

The  Measure  of  Sounds,  as  high  or  low,  is  the  Musical  Scale, 
or  Harmonic  Canon. 

LXXI. 

The  Measures  of  Pure  Colours  are  the  Prismatic  Scale ;  the 
same,  including Fraunhofer1  s  Lines ;  and  Newton's  Scale  of  Colours. 
The  principal  Scales  of  Impure  Colours  are  Werner's  Nomencla- 
ture of  Colours,  and  Merimee^s  Nomenclature  of  Colours. 

LXXII. 

The  Idea  of  Polarity  involves  the  conception  of  contrary  pro- 
perties in  contrary  directions : — the  properties  being,  for  example, 
attraction  and  repulsion,  darkness  and  light,  synthesis  and  analy- 
sis ;  and  the  contrary  directions  being  those  which  are  directly 
opposite,  or,  in  some  cases,  those  which  are  at  right  angles. 


XXX  APHORISMS 

LXXIII.     (Doubtful.) 
Coexistent  polarities  are  fundamentally  identical. 

LXXIV. 

The  Idea  of  Chemical  Affinity,  as  implied  in  Elementary 
Composition,  involves  peculiar  conceptions.  It  is  not  properly 
expressed  by  assuming  the  qualities  of  bodies  to  resemble  those  of 
the  elements,  or  to  depend  on  the  figure  of  the  elements,  or  on 
their  attractions. 

LXXV. 

Attractions  take  place  between  bodies,  affinities  between  the 
particles  of  a  body.  The  former  may  be  compared  to  the  alli- 
ances of  states,  the  latter  to  the  ties  of  family. 

LXXVI. 

The  governing  principles  of  chemical  affinity  are,  that  it  is 
elective ;  that  it  is  definite ;  that  it  determines  the  properties  of  the 
compound;  and  that  analysis  is  possible. 

LXXVII. 

We  have  an  Idea  of  Substance :  and  an  axiom  involved  in  this 
Idea  is,  that  the  weight  of  a  body  is  the  sum  of  the  weights  of  all  its 


LXXVIII. 

Hence  Imponderable  Fluids  are  not  to  be  admitted  as  che- 
mical elements. 

LXXIX. 

The  Doctrine  of  Atoms  is  admissible  as  a  mode  of  expressing 
and  calculating  laws  of  nature ;  but  is  not  proved  by  any  fact, 
chemical  or  physical,  as  a  philosophical  truth. 

LXXX. 

We  have  an  Idea  of  Symmetry ;  and  an  axiom  involved  in  this 
Idea  is,  that  in  a  symmetrical  natural  body,  if  there  be  a  ten- 
dency to  modify  any  member  in  any  manner,  there  is  a  tendency 
to  modify  all  the  corresponding  members  in  the  same  manner. 


CONCERNING    IDEAS.  XXXI 


LXXXI. 

All  hypotheses  respecting  the  manner  in  which  the  elements 
of  inorganic  bodies  are  arranged  in  space,  must  be  constructed 
with  regard  to  the  general  facts  of  crystallization. 

LXXXII. 

When  we  consider  any  object  as  one,  we  give  unity  to  it  by 
an  act  of  thought.  The  condition  which  determines  what  this 
unity  shall  include,  and  what  it  shall  exclude,  is'this ; — that  asser- 
tions concerning  the  one  thing  shall  be  possible. 

LXXXIII. 

We  collect  individuals  into  kinds  by  applying  to  them  the 
Idea  of  Likeness.  Kinds  of  things  are  not  determined  by  defini- 
tions, but  by  this  condition ; — that  general  assertions  concerning 
such  kinds  of  things  shall  be  possible. 

LXXXIV. 

The  names  of  kinds  of  things  are  governed  by  their  use ;  and 
that  may  be  a  right  name  in  one  use  which  is  not  so  in  another. 
A  whale  is  not  a  fish  in  natural  history,  but  it  is  a  fish  in  com- 
merce and  law. 

LXXXV. 

We  take  for  granted  that  each  kind  of  things  has  a  special 
character  which  may  be  expressed  by  a  Definition.  The  ground 
of  our  assumption  is  this ; — that  reasoning  must  be  possible. 

LXXXVI. 

The  "  Five  Words,"  genus,  species,  difference,  property,  acci- 
dent, were  used  by  the  Aristotelians,  in  order  to  express  the  sub- 
ordination of  kinds,  and  to  describe  the  nature  of  definitions  and 
propositions.  In  modern  times,  these  technical  expressions  have 
been  more  referred  to  by  Natural  Historians  than  by  Metaphy- 
sicians. 


XXXII  APHORISMS 

LXXXVII. 

The  construction  of  a  Classificatory  Science  includes  Termi- 
nology,  the  formation  of  a  descriptive  language; — Diataxis,  the 
Plan  of  the  System  of  Classification,  called  also  the  Systematic^ ; — 
Diagnosis,  the  Scheme  of  the  Characters  by  which  the  different 
Classes  are  known,  called  also  the  Characteristic^.  Physiography 
is  the  knowledge  which  the  System  is  employed  to  convey. 
Diataxis  includes  Nomenclature. 

LXXXVIII. 

Terminology  must  be  conventional,  precise,  constant ;  copious 
in  words,  and  minute  in  distinctions,  according  to  the  needs  of 
the  science.  The  student  must  understand  the  terms,  directly 
according  to  the  convention,  not  through  the  medium  of  explana- 
tion or  comparison. 

LXXXIX. 

The  Diataxis,  or  Plan  of  the  System,  may  aim  at  a  Natural 
or  an  Artificial  System.  But  no  classes  can  be  absolutely  arti- 
ficial, for  if  they  were,  no  assertions  could  be  made  concerning 
them. 

XC. 

An  Artificial  System  is  one  in  which  the  smaller  groups  (the 
Genera)  are  natural ;  and  in  which  the  wider  divisions  (Classes, 
Orders)  are  constructed  by  the  peremptory  application  of  selected 
Characters ;  (selected,  however,  so  as  not  to  break  up  the  smaller 
groups.) 

XCI. 

A  Natural  System  is  one  which  attempts  to  make  all  the 
divisions  natural,  the  widest  as  well  as  the  narrowest ;  and  there- 
fore applies  no  characters  peremptorily. 

XCII. 

Natural  Groups  are  best  described,  not  by  any  definition  which 
marks  their  boundaries,  but  by  a  Type  which  marks  their  centre. 
The  Type  of  any  natural  group  is  an  example  which  possesses  in 
a  marked  degree  all  the  leading  characters  of  the  class. 


CONCERNING    IDEAS.  XXX111 


XCIII. 

A  Natural  Group  is  steadily  fixed,  though  not  precisely 
limited ;  it  is  given  in  position,  though  not  circumscribed ;  it  is 
determined,  not  by  a  boundary  without,  but  by  a  central  point 
within ; — not  by  what  it  strictly  excludes,  but  by  what  it  emi- 
nently includes ; — by  a  Type,  not  by  a  Definition. 

XCIV. 

The  prevalence  of  Mathematics  as  an  element  of  education 
has  made  us  think  Definition  the  philosophical  mode  of  fixing  the 
meaning  of  a  word :  if  (Scientific)  Natural  History  were  intro- 
duced into  education,  men  might  become  familiar  with  the  fixa- 
tion of  the  signification  of  words  by  Types ;  and  this  agrees  more 
nearly  with  the  common  processes  by  which  words  acquire  their 
significations. 

xcv. 

The  attempts  at  Natural  Classification  are  of  three  sorts; 
according  as  they  are  made  by  the  process  of  blind  trial,  of  general 
comparison,  or  of  subordination  of  characters.  The  process  of 
Blind  Trial  professes  to  make  its  classes  by  attention  to  all  the 
characters,  but  without  proceeding  methodically.  The  process  of 
General  Comparison  professes  to  enumerate  all  the  characters,  and 
forms  its  classes  by  the  majority.  Neither  of  these  methods  can 
really  be  carried  into  effect.  The  method  of  Subordination  of 
Characters  considers  some  characters  as  more  important  than 
others ;  and  this  method  gives  more  consistent  results  than  the 
others.  This  method,  however,  does  not  depend  upon  the  Idea 
of  Likeness  only,  but  introduces  the  Idea  of  Organization  or 
Function. 

XCVI. 

A  Species  is  a  collection  of  individuals  which  are  descended 
from  a  common  stock,  or  which  resemble  such  a  collection  as 
much  as  these  resemble  each  other :  the  resemblance  being 
opposed  to  a  definite  difference. 


XXXIV  APHORISMS 

XCVII. 

A  Genus  is  a  collection  of  species  which  resemble  each  other 
more  than  they  resemble  other  species :  the  resemblance  being 
opposed  to  a  definite  difference. 

XCVIII. 

The  Nomenclature  of  a  Classificatory  Science  is  the  collection 
of  the  names  of  the  Species,  Genera,  and  other  divisions.  The 
binary  nomenclature,  which  denotes  a  species  by  the  generic  and 
specific  name,  is  now  commonly  adopted  in  Natural  History. 

XCIX. 

The  Diagnosis,  or  Scheme  of  the  Characters,  comes,  in  the 
order  of  philosophy,  after  the  Classification.  The  characters  do 
not  make  the  classes,  they  only  enable  us  to  recognize  them.  The 
Diagnosis  is  an  Artificial  Key  to  a  Natural  System. 

C. 

The  basis  of  all  Natural  Systems  of  Classification  is  the  Idea 
of  Natural  Affinity.  The  Principle  which  this  Idea  involves  is 
this : — Natural  arrangements,  obtained  from  different  sets  of  cha- 
racters, must  coincide  with  each  other. 

CI. 

In  order  to  obtain  a  Science  of  Biology,  we  must  analyse  the 
Idea  of  Life.  It  has  been  proved  by  the  biological  speculations 
of  past  time,  that  organic  Life  cannot  rightly  be  resolved  into 
mechanical  or  chemical  forces,  or  the  operation  of  a  vital  fluid,  or 
of  a  soul. 

CII. 

Life  is  a  System  of  Vital  Forces ;  and  the  conception  of  such 
Forces  involves  a  peculiar  Fundamental  Idea. 

cm. 

Mechanical,  chemical,  and  vital  Forces  form  an  ascending 
progression,  each  including  the  preceding.  Chemical  Affinity 


CONCERNING    IDEAS.  XXXV 

includes  in  its  nature  Mechanical  Force,  and  may  often  be  prac- 
tically resolved  into  Mechanical  Force.  (Thus  the  ingredients  of 
gunpowder,  liberated  from  their  chemical  union,  exert  great 
mechanical  Force :  a  galvanic  battery  acting  by  chemical  pro- 
cess does  the  like.)  Vital  Forces  include  in  their  nature  both 
chemical  Affinities  and  mechanical  Forces :  for  Vital  Powers 
produce  both  chemical  changes,  (as  digestion,)  and  motions  which 
imply  considerable  mechanical  force,  (as  the  motion  of  the  sap 
and  of  the  blood.) 

CIV. 

In  voluntary  motions,  Sensations  produce  Actions,  and  the 
connexion  is  made  by  means  of  Ideas  :  in  reflected  motions,  the 
connexion  neither  seems  to  be  nor  is  made  by  means  of  Ideas :  in 
instinctive  motions,  the  connexion  is  such  as  requires  Ideas,  but 
we  cannot  believe  the  Ideas  to  exist. 

CV. 

The  assumption  of  a  Final  Cause  in  the  structure  of  each  part 
of  animals  and  plants  is  as  inevitable  as  the  assumption  of  an 
Efficient  Cause  for  every  event.  The  maxim  that  in  organized 
bodies  nothing  is  in  vain,  is  as  necessarily  true  as  the  maxim  that 
nothing  happens  by  chance. 

CVI. 

The  idea  of  living  beings  as  subject  to  disease  includes  a 
recognition  of  a  Final  Cause  in  organization ;  for  disease  is  a 
state  in  which  the  vital  forces  do  not  attain  their  proper  ends. 

CVII. 

The  Palsetiological  Sciences  depend  upon  the  Idea  of  Cause ; 
but  the  leading  conception  which  they  involve  is  that  of  historical 
cause,  not  mechanical  cause. 

CVIII. 

Each  Palsetiological  Science,  when  complete,  must  possess 
three  members :  the  Phenomenology,  the  ^Etiology >,  and  the 
Theory. 


XXXVI  APHORISMS    CONCERNING   IDEAS. 

CIX. 

There  are,  in  the  Palsetiological  Sciences,  two  antagonist  doc- 
trines :  Catastrophes  and  Uniformity.  The  doctrine  of  a  uniform 
course  of  nature  is  tenable  only  when  we  extend  the  notion  of 
uniformity  so  far  that  it  shall  include  catastrophes. 

CX. 

The  Catastrophist  constructs  Theories,  the  Uniformitarian 
demolishes  them.  The  former  adduces  evidence  of  an  Origin,  the 
latter  explains  the  evidence  away.  The  Catastrophist's  dogmatism 
is  undermined  by  the  Uniformitarian'>s  skeptical  hypotheses. 
But  when  these  hypotheses  are  asserted  dogmatically,  they  cease 
to  be  consistent  with  the  doctrine  of  uniformity. 

CXI. 

In  each  of  the  Palsetiological  Sciences,  we  can  ascend  to 
remote  periods  by  a  chain  of  causes,  but  in  none  can  we  ascend 
to  a  beginning  of  the  chain. 

CXII. 

In  contemplating  the  series  of  causes  and  effects  which  con- 
stitutes the  world,  we  necessarily  assume  a  First  Cause  of  the 
whole  series. 

CXIII. 

The  Palaetiological  Sciences  point  backwards  with  lines  which 
are  broken,  but  which  all  converge  to  the  same  invisible  point : 
and  this  point  is  the  Origin  of  the  Moral  and  Spiritual,  as  well  as 
of  the  natural  world. 


XXXV11 


APHORISMS  CONCERNING  SCIENCE. 


I. 

The  two  processes  by  which  Science  is  constructed  are  the 
Explication  of  Conceptions  and  the  Colligation  of  Facts. 

II. 

The  Explication  of  Conceptions,  as  requisite  for  the  progress 
of  science,  has  been  effected  by  means  of  discussions  and  contro- 
versies among  scientists ;  often  by  debates  concerning  definitions ; 
these  controversies  have  frequently  led  to  the  establishment  of  a 
Definition  ;  but  along  with  the  Definition,  a  corresponding  Pro- 
position has  always  been  expressed  or  implied.  The  essential 
requisite  for  the  advance  of  science  is  the  clearness  of  the  Concep- 
tion, not  the  establishment  of  a  Definition.  The  construction  of 
an  exact  Definition  is  often  very  difficult.  The  requisite  condi- 
tions of  clear  Conceptions  may  often  be  expressed  by  Axioms  as 
well  as  by  Definitions. 

III. 

Conceptions,  for  purposes  of  science,  must  be  appropriate  as 
well  as  clear :  that  is,  they  must  be  modifications  of  that  Funda- 
mental Idea,  by  which  the  phenomena  can  really  be  interpreted. 
This  maxim  may  warn  us  from  error,  though  it  may  not  lead  to 
discovery.  Discovery  depends  upon  the  previous  cultivation  or 
natural  clearness  of  the  appropriate  Idea,  and  therefore  no  dis- 
covery is  the  work  of  accident. 

IV. 

Facts  are  the  materials  of  science,  but  all  Facts  involve  Ideas. 
Since,  in  observing  Facts,  we  cannot  exclude  Ideas,  we  must,  for 
the  purposes  of  science,  take  care  that  the  Ideas  are  clear  and 
rigorously  applied. 


XXXVlli  APHORISMS 


V. 

The  last  Aphorism  leads  to  such  Rules  as  the  following : — 
That  Facts,  for  the  purposes  of  material  science,  must  involve 
Conceptions  of  the  Intellect  only,  and  not  Emotions  : — That  Facts 
must  be  observed  with  reference  to  our  most  exact  conceptions, 
Number,  Place,  Figure,  Motion : — That  they  must  also  be  ob- 
served with  reference  to  any  other  exact  conceptions  which  the 
phenomena  suggest,  as  Force,  in  mechanical  phenomena,  Concord, 
in  musical. 

VI. 

The  resolution  of  complex  Facts  into  precise  and  measured 
partial  Facts,  we  call  the  Decomposition  of  Facts.  This  process 
is  requisite  for  the  progress  of  science,  but  does  not  necessarily 
lead  to  progress. 

VII 

Science  begins  with  common  observation  of  facts  ;  but  even  at 
this  stage,  requires  that  the  observations  be  precise.  Hence  the 
sciences  which  depend  upon  space  and  number  were  the  earliest 
formed.  After  common  Observation,  come  scientific  Observation 
and  Experiment . 

VIII. 

The  Conceptions  by  which  Facts  are  bound  together,  are  sug- 
gested by  the  sagacity  of  discoverers.  This  sagacity  cannot  be 
taught.  It  commonly  succeeds  by  guessing;  and  this  success 
seems  to  consist  in  framing  several  tentative  hypotheses  and  select- 
ing the  right  one.  But  a  supply  of  appropriate  hypotheses  cannot 
be  constructed  by  rule,  nor  without  inventive  talent. 

IX. 

The  truth  of  tentative  hypotheses  must  be  tested  by  their 
application  to  facts.  The  discoverer  must  be  ready,  carefully  to 
try  his  hypotheses  in  this  manner,  and  to  reject  them  if  they  will 
not  bear  the  test,  in  spite  of  indolence  and  vanity. 


CONCERNING   SCIENCE.  XXXIX 

X. 

The  process  of  scientific  discovery  is  cautious  and  rigorous,  not 
by  abstaining  from  hypotheses,  but  by  rigorously  comparing 
hypotheses  with  facts,  and  by  resolutely  rejecting  all  which  the 
comparison  does  not  confirm. 

XL 

Hypotheses  may  be  useful,  though  involving  much  that  is 
superfluous,  and  even  erroneous  :  for  they  may  supply  the  true 
bond  of  connexion  of  the  facts  ;  and  the  superfluity  and  error  may 
afterwards  be  pared  away. 

XII. 

It  is  a  test  of  true  theories  not  only  to  account  for,  but  to 
predict  phenomena. 

XIII. 

« 

Induction  is  a  term  applied  to  describe  the  process  of  a  true 
Colligation  of  Facts  by  means  of  an  exact  and  appropriate  Con- 
ception. An  Induction  is  also  employed  to  denote  the  proposition 
which  results  from  this  process. 

XIV. 

The  Consilience  of  Inductions  takes  place  when  an  Induction, 
obtained  from  one  class  of  facts,  coincides  with  an  Induction, 
obtained  from  another  different  class.  This  Consilience  is  a  test 
of  the  truth  of  the  Theory  in  which  it  occurs. 

XV. 

An  Induction  is  not  the  mere  sum  of  the  Facts  which  are 
colligated.  The  Facts  are  not  only  brought  together,  but  seen  in 
a  new  point  of  view.  A  new  mental  Element  is  superinduced ; 
and  a  peculiar  constitution  and  discipline  of  mind  are  requisite  in 
order  to  make  this  Induction. 

XVI. 

Although  in  Every  Induction  a  new  conception  is  superin- 
duced upon  thfr  Facts  ;  yet  this  once  effectually  done,  the  novelty 


XL  APHORISMS 

of  the  conception  is  overlooked,  and  the  conception  is  considered 
as  a  part  of  the  fact. 

XVII. 

The  Logic  of  Induction  consists  in  stating  the  Facts  and  the 
Inference  in  such  a  manner,  that  the  evidence  of  the  Inference  is 
manifest ;  just  as  the  Logic  of  Deduction  consists  in  stating  the 
Premises  and  the  Conclusion  in  such  a  manner  that  the  Evidence 
of  the  Conclusion  is  manifest. 

XVIII. 

The  Logic  of  Deduction  is  exhibited  by  means  of  a  certain 
Formula ;  namely,  a  Syllogism ;  and  every  train  of  deductive 
reasoning,  to  be  demonstrative,  must  be  capable  of  resolution  into 
a  series  of  such  Formulae  legitimately  constructed.  In  like  man- 
ner, the  Logic  of  Induction  may  be  exhibited  by  means  of  certain 
Formulas  ,•  and  every  train  of  inductive  inference,  to  be  sound, 
must  be  capable  of  resolution  into  a  scheme  of  such  Formulae, 
legitimately  constructed. 

XIX. 

The  inductive  act  of  thought  by  which  several  Facts  are  col- 
ligated into  one  Proposition,  may  be  expressed  by  saying  :  The 
several  Facts  are  exactly  expressed  as  onetFact,  if,  and  only  if,  we 
adopt  the  Conceptions  and  the  Assertion  of  the  Proposition. 

XX. 

The  One  Fact,  thus  inductively  obtained  from  several  Facts, 
may  be  combined  with  other  Facts,  and  colligated  with  them 
by  a  new  act  of  Induction.  This  process  may  be  indefinitely 
repeated  :  and  these  successive  processes  are  the  Steps  of  Induc- 
tion, or  of  Generalization,  from  the  lowest  to  the  highest. 

XXL 

The  relation  of  the  successive  Steps  of  Induction  may  be 
exhibited  by  means  of  an  Inductive  Table,  in  which  the  several 
Facts  are  indicated,  and  tied  together  by  a  Bracket,  and  the  In- 
ductive Inference  placed  on  the  other  side  of  the  Bracket ;  and 


CONCERNING  SCIENCE.  XLi 

this  arrangement  repeated,  so  as  to  form  a  genealogical  Table  of 
each  Induction,  from  the  lowest  to  the  highest. 

XXII. 

The  Logic  of  Induction  is  the  Criterion  of  Truth  inferred 
from  Facts,  as  the  Logic  of  Deduction  is  the  Criterion  of  Truth 
deduced  from  necessary  Principles.  The  Inductive  Table  enables 
us  to  apply  such  a  Criterion  ;  for  we  can  determine  whether  each 
Induction  is  verified  and  justified  by  the  Facts  which  its  Bracket 
includes;  and  if  each  induction  in  particular  be  sound,  the 
highest,  which  merely  combines  them  all,  must  necessarily  be 

sound  also. 

XXIII. 

The  distinction  of  Fact  and  Theory  is  only  relative.  Events 
and  phenomena,  considered  as  particulars  which  may  be  colligated 
by  Induction,  are  Facts ;  considered  as  generalities  already  ob- 
tained by  colligation  of  other  Facts,  they  are  Theories.  The 
same  event  or  phenomenon  is  a  Fact  or  a  Theory,  according  as  it 
is  considered  as  standing  on  one  side  or  the  other  of  the  Inductive 

Bracket. 

XXIV. 

Inductive  truths  are  of  two  kinds,  Laws  of  Phenomena,  and 
Theories  of  Causes.  It  is  necessary  to  begin  in  every  science 
with  the  Laws  of  Phenomena;  but  it  is  impossible  that  we 
should  be  satisfied  to  stop  short  of  a  Theory  of  Causes.  In  Phy- 
sical Astronomy,  Physical  Optics,  Geology,  and  other  sciences, 
we  have  instances  showing  that  we  can  make  a  great  advance  in 
inquiries  after  true  Theories  of  Causes. 

XXV. 

Art  and  Science  differ.  The  object  of  Science  is  Knowledge; 
the  objects  of  Art,  are  Works.  In  Art,  truth  is  a  means  to  an 
end  ;  in  Science,  it  is  the  only  end.  Hence  the  Practical  Arts  are 
not  to  be  classed  among  the  Sciences. 

XXVI. 

Practical  Knowledge,  such  as  Art  implies,  is  not  Knowledge 
such  as  Science  includes.     Brute  animals  have  a  practical  know- 
VOL.  I.  d 


XL11  APHORISMS 

ledge  of  relations  of  space  and  force ;  but  they  have  no  know- 
ledge of  Geometry  or  Mechanics. 

XXVII. 

The  Methods  by  which  the  construction  of  Science  is  pro- 
moted are,  Methods  of  Observation,  Methods  of  obtaining  clear 
Ideas,  and  Methods  of  Induction. 

XXVIII. 

The  Methods  of  Observation  of  Quantity  in  general,  are 
Numeration,  which  is  precise  by  the  nature  of  Number;  the 
Measurement  of  Space  and  of  Time,  which  are  easily  made  pre- 
cise ;  the  Conversion  of  Space  and  Time,  by  which  each  aids  the 
measurement  of  the  other ;  the  Method  of  Repetition ;  the 
Method  of  Coincidences  or  Interferences.  The  measurement  of 
Weight  is  made  precise  by  the  Method  of  Double-weighing. 
Secondary  Qualities  are  measured  by  means  of  Scales  of  Degrees ; 
but  in  order  to  apply  these  Scales,  the  student  requires  the  Edu- 
cation of  the  Senses.  The  Education  of  the  Senses  is  forwarded 
by  the  practical  study  of  Descriptive  Natural  History,  Chemical 
Manipulation,  and  Astronomical  Observation. 

XXIX. 

The  Methods  by  which  the  acquisition  of  clear  Scientific 
Ideas  is  promoted,  are  mainly  two ;  Intellectual  Education  and 
Discussion  of  Ideas. 

XXX. 

The  Idea  of  Space  becomes  more  clear  by  studying  Geometry; 
the  Idea  of  Force,  by  studying  Mechanics;  the  Ideas  of  Likeness, 
of  Kind,  of  subordination  of  Classes,  by  studying  Natural  History. 

XXXI. 

Elementary  Mechanics  should  now  form  a  part  of  intellectual 
education,  in  order  that  the  student  may  understand  the  Theory 
of  Universal  Gravitation  :  for  an  intellectual  education  should 
cultivate  such  ideas  as  enable  the  student  to  understand  the 
most  complete  and  admirable  portions  of  the  knowledge  which 
the  human  race  has  attained  to. 


CONCERNING    SCIENCE. 

XXXII. 

Natural  History  ought  to  form  a  part  of  intellectual  educa- 
tion, in  order  to  correct  certain  prejudices  which  arise  from  cul- 
tivating the  intellect  by  means  of  mathematics  alone-;  and  in 
order  to  lead  the  student  to  see  that  the  division  of  things  into 
kinds,  and  the  attribution  and  use  of  names,  are  processes  sus- 
ceptible of  great  precision. 

XXXIII. 

The  conceptions  involved  in  scientific  truths  have  attained 
the  requisite  degree  of  clearness  by  means  of  the  Discussions 
respecting  ideas  which  have  taken  place  among  discoverers 
and  their  followers.  Such  discussions  are  very  far  from  being 
unprofitable  to  science.  They  are  metaphysical,  and  must  be  so : 
the  difference  between  discoverers  and  barren  reasoners  is,  that 
the  former  employ  good,  and  the  latter  bad  metaphysics. 

XXXIV. 

The  Process  of  Induction  may  be  resolved  into  three  steps ; 
the  Selection  of  the  Idea,  the  Construction  of  the  Conception,  and 
the  Determination  of  the  Magnitudes. 

XXXV. 

These  three  steps  correspond  to  the  determination  of  the  In- 
dependent variable,  the  Formula,  and  the  Coefficients,  in  mathema- 
tical investigations;  or  to  the  Argument,  the  Law,  and  the 
Numerical  Data,  in  a  Table  of  an  Inequality. 

XXXVI. 

The  Selection  of  the  Idea  depends  mainly  upon  inventive 
sagacity  :  which  operates  by  suggesting  and  trying  various  hypo- 
theses. Some  inquirers  try  erroneous  hypotheses;  and  thus, 
exhausting  the  forms  of  error,  form  the  Prelude  to  Discovery. 

XXXVII. 

The  following  Rules  may  be  given,  in  order  to  the  selection 
of  the  Idea  for  purposes  of  Induction : — the  Idea  and  the  Facts 
must  be  homogeneous ;  and  the  Rule  must  be  tested  by  the  Facts. 

d  2 


XL1V  APHORISMS 

XXXVIII. 

The  Construction  of  the  Conception  very  often  includes,  in  a 
great  measure,  the  Determination  of  the  Magnitudes. 

XXXIX. 

When  a  series  of  progressive  numbers  is  given  as  the  rasult 
of  observation,  it  may  generally  be  reduced  to  law  by  combina- 
tions of  arithmetical  and  geometrical  progressions. 

XL. 

A  true  formula  for  a  progressive  series  of  numbers  cannot 
commonly  be  obtained  from  a  narrow  range  of  observations. 

XLI. 

Recurrent  series  of  numbers  must,  in  most  cases,  be  expressed 
by  circular  formulae. 

XLII. 

The  true  construction  of  the  conception  is  frequently  sug- 
gested by  some  hypothesis ;  and  in  these  cases,  the  hypothesis 
may  be  useful,  though  containing  superfluous  parts. 

XLIII. 

There  are  special  Methods  of  Induction  applicable  to  Quan- 
tity ;  of  which  the  principal  are,  the  Method  of  Curves,  the 
Method  of  Means,  the  Method  of  Least  Squares,  and  the  Method 
of  Residues. 

XLIV. 

The  Method  of  Curves  consists  in  drawing  a  curve,  of  which 
the  observed  quantities  are  the  ordinates,  the  quantity  on  which 
the  change  of  these  quantities  depends  being  the  abscissa.  Its 
efficacy  depends  upon  the  faculty  which  the  eye  possesses,  of 
readily  detecting  regularity  and  irregularity  in  forms.  It  may  be 
used  to  detect  the  laws  which  the  observed  quantities  follow ; 
and  also,  when  the  observations  are  inexact,  it  may  be  used  to 
correct  these  observations,  so  as  to  obtain  data  more  true  than  the 
observed  facts  themselves. 


CONCERNING    SCIENCE.  XLV 

XLV. 

The  Method  of  Means  gets  rid  of  irregularities  by  taking  the 
arithmetical  mean  of  a  great  number  of  observed  quantities.  Its 
efficacy  depends  upon  this  ;  that  in  cases  in  which  observed  quan- 
tities are  affected  by  other  inequalities,  besides  that  of  which  we 
wish  to  determine  the  law,  the  excesses  above  and  defects  below 
the  quantities  which  the  law  in  question  would  produce,  will,  in 
a  collection  of  many  observations,  balance  each  other. 

XLVI. 

The  Method  of  Least  Squares  is  a  Method  of  Means,  in  which 
the  mean  is  taken  according  to  the  condition,  that  the  sum  of  the 
squares  of  the  errors  of  observation  shall  be  the  least  possible 
which  the  law  of  the  facts  allows.  It  appears,  by  the  doctrine  of 
chances,  that  this  is  the  most  probable  mean. 

XLVII. 

The  Method  of  Residues  consists  in  subtracting,  from  the  quan- 
tities given  by  observation,  the  quantity  given  by  any  law  already 
discovered ;  and  then  examining  the  remainder,  or  Residue,  in 
order  to  discover  the  leading  law  which  it  follows.  When  this 
second  law  has  been  discovered,  the  quantity  given  by  it  may  be 
subtracted  from  the  first  Residue ;  thus  giving  a  Second  Residue, 
which  may  be  examined  in  the  same  manner ;  and  so  on.  The 
efficacy  of  this  method  depends  principally  upon  the  circumstance 
of  the  laws  of  variation  being  successively  smaller  and  smaller  in 
amount  (or  at  least  in  their  mean  effect)  ;  so  that  the  ulterior 
undiscovered  laws  do  not  prevent  the  law  in  question  from  being 
prominent  in  the  observations. 

XLVIII. 

The  Method  of  Means  and  the  Method  of  Least  Squares  can- 
not be  applied  without  our  knowing  the  Arguments  of  the  Inequa- 
lities which  we  seek.  The  Method  of  Curves  and  the  Method  of 
Residues,  when  the  Arguments  of  the  principal  Inequalities  are 
known,  often  make  it  easy  to  find  the  others. 


XLY1  APHORISMS 


XLIX. 

The  Law  of  Continuity  is  this  : — that  a  quantity  cannot  pass 
from  one  amount  to  another  by  any  change  of  conditions,  without 
passing  through  all  intermediate  magnitudes  according  to  the 
intermediate  conditions.  It  may  often  be  employed  to  disprove 
distinctions  which  have  no  real  foundation. 

L. 

The  Method  of  Gradation  consists  in  taking  a  number  of  stages 
of  a  property  in  question,  intermediate  between  two  extreme 
cases  which  appear  to  be  different.  It  is  employed  to  determine 
whether  the  extreme  cases  are  really  distinct  or  not. 

LI. 

The  Method  of  Gradation,  applied  to  decide  the  question, 
whether  the  existing  geological  phenomena  arise  from  existing 
causes,  leads  to  this  result :— That  the  phenomena  do  appear  to 
arise  from  existing  causes,  but  that  the  action  of  existing  causes 
may,  in  past  times,  have  transgressed,  to  any  extent,  their 
recorded  limits  of  intensity. 

LIL 

The  Method  of  Natural  Classification  consists  in  classing 
cases,  not  according  to  any  assumed  definition,  but  according  to 
the  connexion  of  the  facts  themselves,  so  as  to  make  them  the 
means  of  asserting  general  truths. 

LIII. 

In  the  Induction  of  Causes  the  principal  maxim  is,  that  we 
must  be  careful  to  possess,  and  to  apply,  with  perfect  clearness, 
the  Fundamental  Idea  on  which  the  Induction  depends. 

LIV. 

The  Induction  of  Substance,  of  Force,  of  Polarity,  go  beyond 
mere  laws  of  phenomena,  and  may  be  considered  as  the  Induction 
cf  Causes. 


CONCERNING   SCIENCE.  XLvii 

LV. 

The  Cause  of  certain  phenomena  being  inferred,  we  are  led  to 
inquire  into  the  Cause  of  this  Cause,  which  inquiry  must  be  con- 
ducted in  the  same  manner  as  the  previous  one ;  and  thus  we 
have  the  Induction  of  Ulterior  Causes. 

LVI. 

In  contemplating  the  series  of  Causes  which  are  themselves 
the  effects  of  other  causes,  we  are  necessarily  led  to  assume  a 
Supreme  Cause  in  the  Order  of  Causation,  as  we  assume  a  First 
Cause  in  Order  of  Succession. 


XLY111 

APHORISMS 
CONCERNING  THE  LANGUAGE  OF  SCIENCE. 


INTRODUCTION. 

IT  has  been  shown  in  the  History  of  Science,  and  will 
further  appear  in  the  course  of  the  present  work,  that  almost 
every  step  in  the  progress  of  science  is  marked  by  the  formation 
or  appropriation  of  a  technical  term.  Common  language  has, 
in  most  cases,  a  certain  degree  of  looseness  and  ambiguity ;  as 
common  knowledge  has  usually  something  of  vagueness  and 
indistinctness.  In  common  cases  too,  knowledge  usually  does 
not  occupy  the  intellect  alone,  but  more  or  less  interests  some 
affection,  or  puts  in  action  the  fancy ;  and  common  language, 
accommodating  itself  to  the  office  of  expressing  such  knowledge, 
contains,  in  every  sentence,  a  tinge  of  emotion  or  of  imagina- 
tion. But  when  our  knowledge  becomes  perfectly  exact  and 
purely  intellectual,  we  require  a  language  which  shall  also  be 
exact  and  intellectual ; — which  shall  exclude  alike  vagueness  and 
fancy,  imperfection  and  superfluity ; — in  which  each  term  shall 
convey  a  meaning  steadily  fixed  and  rigorously  limited.  Such  a 
language  that  of  science  becomes  through  the  use  of  technical 
terms.  And  we  must  now  endeavour  to  lay  down  some  maxims 
and  suggestions,  by  attention  to  which  technical  terms  may  be 
better  fitted  to  answer  their  purpose.  In  order  to  do  this,  we 
shall  in  the  first  place  take  a  rapid  survey  of  the  manner  in 
which  technical  terms  have  been  employed  from  the  earliest 
periods  of  scientific  history. 

The  progress  of  the  use  of  technical  scientific  language  offers 
to  our  notice  two  different  and  successive  periods ;  in  the  first  of 
which,  technical  terms  were  formed  casually,  as  convenience  in 


THE   LANGUAGE    OF    SCIENCE.  XIJX 

each  case  prompted ;  while  in  the  second  period,  technical  lan- 
guage was  constructed  intentionally,  with  set  purpose,  with  a 
regard  to  its  connexion,  and  with  a  view  of  constructing  a  system. 
Though  the  casual  and  systematic  formation  of  technical  terms 
cannot  be  separated  by  any  precise  date  of  time,  (for  at  all  periods 
some  terms  in  some  sciences  have  been  framed  unsystematically,) 
we  may,  as  a  general  description,  call  the  former  the  ancient  and 
the  latter  the  modern  period.  In  illustrating  the  two  following 
Aphorisms,  I  will  give  examples  of  the  course  followed  in  each 
of  these  periods. 

APHORISM  I. 

In  the  Ancient  Period  of  Science,  Technical  Terms  were  formed  in 
three  different  ways: — by  appropriating  common  words  and 
fixing  their  meaning; — by  constructing  terms  containing  a 
description ; — by  constructing  terms  containing  reference  to  a 
theory. 

THE  earliest  sciences  offer  the  earliest  examples  of  technical 
terms.  These  are  Geometry,  Arithmetic,  and  Astronomy;  to 
which  we  have  soon  after  to  add  Harmonics,  Mechanics,  and 
Optics.  In  these  sciences,  we  may  notice  the  above-mentioned 
three  different  modes  in  which  technical  terms  were  formed. 

I.  The  simplest  and  first  mode  of  acquiring  technical  terms, 
is  to  take  words  current  in  common  usage,  and  by  rigorously 
defining  or  otherwise  fixing  their  meaning,  to  fit  them  for  the 
expression  of  scientific  truths.  In  this  manner  almost  all 
the  fundamental  technical  terms  of  Geometry  were  formed. 
A  sphere,  a  cone,  a  cylinder,  had  among  the  Greeks,  at  first, 
meanings  less  precise  than  those  which  geometers  gave  to 
these  words,  and  besides  the  mere  designation  of  form,  implied 
some  use  or  application.  A  sphere  (cr<f>alpa)  was  a  hand-ball 
used  in  games;  a  cone  (KWVOS)  was  a  boy's  spinning-top,  or  the 
crest  of  a  helmet ;  a  cylinder  (fcv\wSpos)  was  a  roller ;  a  cube 
(tcvftos)  was  a  die  :  till  these  words  were  adopted  by  the  geo- 
meters, and  made  to  signify  among  them  pure  modifications  of 


t,  APHORISMS   CONCERNING 

space.  So  an  angle  (ywvia)  was  only  a  corner  ; 
was  a  signal ;  a  line  (ypapprj)  was  a  mark ;  a  straight  line 
(evOela)  was  marked  by  an  adjective  which  at  first  meant  only 
direct.  A  plane  (eV/TreSoy)  is  the  neuter  form  of  an  adjective, 
which  by  its  derivation  means  on  the  ground,  and  hence  flat.  In 
all  these  cases,  the  word  adopted  as  a  term  of  science  has  its 
sense  rigorously  fixed  ;  and  where  the  common  use  of  the  term  is 
in  any  degree  vague,  its  meaning  may  be  modified  at  the  same 
time  that  it  is  thus  limited.  Thus  a  rhombus  (po^fios)  by  its 
derivation,  might  mean  any  figure  which  is  ticisted  out  of  a  regular 
form ;  but  it  is  confined  by  geometers  to  that  figure  which  has 
four  equal  sides,  its  angles  being  oblique.  In  like  manner,  a  tra- 
pezium (rpaTretyov)  originally  signifies  a  table,  and  thus  might 
denote  any  form ;  but  as  the  tables  of  the  Greeks  had  one  side 
shorter  than  the  opposite  one,  such  a  figure  was  at  first  called  a 
trapezium.  Afterwards  the  term  was  made  to  signify  any  figure 
with  four  unequal  sides ;  a  name  being  more  needful  in  geometry 
for  this  kind  of  figure  than  for  the  original  form. 

This  class  of  technical  terms,  namely,  words  adopted  from 
common  language,  but  rendered  precise  and  determinate  for  pur- 
poses of  science,  may  also  be  exemplified  in  other  sciences.  Thus, 
as  was  observed  in  the  early  portion  of  the  history  of  astronomy  *, 
a  day,  a  month,  a  year,  described  at  first  portions  of  time  marked 
by  familiar  changes,  but  afterwards  portions  determined  by  rigor- 
ous mathematical  definitions.  The  conception  of  the  heavens  as 
a  revolving  sphere,  is  so  obvious,  that  we  may  consider  the  terms 
which  involve  this  conception  as  parts  of  common  language ;  as 
the  pole  (TTO\OS)  of  the  arctic  circle,  which  includes  the  stars  that 
never  set-)-;  the  horizon  (6pl£cov)  a  boundary,  applied  technically 
to  the  circle  bounding  the  visible  earth  and  sky.  The  turnings 
of  the  sun  (rpoTral  rjeXloio),  which  are  mentioned  by  Hesiod,  gave 
occasion  to  the  term  tropics,  the  circles  at  which  the  sun  in  his 
annual  motion  turns  back  from  his  northward  or  southward  advance. 
The  zones  of  the  earth,  (the  torrid,  temperate,  and  frigid ;)  the 
gnomon  of  a  dial ;  the  limb  (or  border)  of  the  moon,  or  of  a  circular 

*  Hist.  Ind.  Set.,  i.  112.  t  Hist.  Ast.,  i.  144. 


THE   LANGUAGE   OF   SCIENCE.  Ll 


instrument,  are  terms  of  the  same  class.  An  eclipse  (&X{f^if)  is 
originally  a  deficiency  or  disappearance,  and  joined  with  the  name 
of  the  luminary,  an  eclipse  of  the  sun  or  of  the  moon,  described 
the  phenomenon  ;  but  when  the  term  became  technical,  it  suf- 
ficed, without  addition,  to  designate  the  phenomenon. 

In  Mechanics,  the  Greeks  gave  a  scientific  precision  to  very 
few  words  :  we  may  mention  weights  (ftapea),  the  arms  of  a  lever 
(^'%ea),  its  fulcrum  (uTroyu-o^XtW),  and  the  verb  to  balance 
(lo-oppoirelv).  Other  terms  which  they  used,  as  momentum 
(poTrrj)  said,  force  (Swa/jus),  did  not  acquire  a  distinct  and  definite 
meaning  till  the  time  of  Galileo,  or  later.  We  may  observe  that 
all  abstract  terms,  though  in  their  scientific  application  expressing 
mere  conceptions,  were  probably  at  first  derived  from  some  word 
describing  external  objects.  Thus  the  Latin  word  for  force,  vis, 
seems  to  be  connected  with  a  Greek  word,  is,  or  Fls,  which  often 
has  nearly  the  same  meaning  ;  but  originally,  as  it  would  seem, 
signified  a  sinew  or  muscle,  the  obvious  seat  of  animal  strength. 

In  later  times,  the  limitation  imposed  upon  a  word  by  its 
appropriation  to  scientific  purposes,  is  often  more  marked  than 
in  the  cases  above  described.  Thus  the  variation  is  made  to 
mean,  in  astronomy,  the  second  inequality  of  the  moon's  motion  ; 
in  magnetism,  the  variation  signifies  the  angular  deviation  of  the 
compass-needle  from  the  north  ;  in  pure  mathematics,  the  varia- 
tion of  a  quantity  is  the  formula  which  expresses  the  result  of  any 
small  change  of  the  most  general  kind.  In  like  manner,  parallax 
(TrapaXXagis)  denotes  a  change  in  general,  but  is  used  by  astro- 
nomers to  signify  the  change  produced  by  the  spectator's  being 
removed  from  the  centre  of  the  earth,  his  theoretical  place,  to  the 
surface.  Alkali  at  first  denoted  the  ashes  of  a  particular  plant, 
but  afterwards,  all  bodies  having  a  certain  class  of  chemical  pro- 
perties ;  and,  in  like  manner,  acid,  the  class  opposed  to  alkali, 
was  modified  in  signification  by  chemists,  so  as  to  refer  no  longer 
to  the  taste. 

Words  thus  borrowed  from  common  language,  and  converted 
by  scientific  writers  into  technical  terms,  have  some  advantages 
and  some  disadvantages.  They  possess  this  great  convenience, 
that  they  are  understood  after  a/  very  short  explanation,  and 


Lll  APHORISMS    CONCERNING 

retained  in  the  memory  without  effort.  On  the  other  hand,  they 
lead  to  some  inconvenience ;  for  since  they  have  a  meaning!  in 
common  language,  a  careless  reader  is  prone  to  disregard  the 
technical  limitation  of  this  meaning,  and  to  attempt  to  collect 
their  import  in  scientific  hooks,  in  the  same  vague  and  conjectural 
manner  in  which  he  collects  the  purpose  of  words  in  common 
cases.  Hence  the  language  of  science,  when  thus  resembling 
common  language,  is  liable  to  be  employed  with  an  absence  of  that 
scientific  precision  which  alone  gives  it  value.  Popular  writers 
and  talkers,  when  they  speak  of  force,  momentum,  action  and 
reaction,  and  the  like,  often  afford  examples  of  the  inaccuracy 
thus  arising  from  the  scientific  appropriation  of  common  terms. 

II.  Another  class  of  technical  terms,  which  we  find  occurring 
as  soon  as  speculative  science  assumes  a  distinct  shape,  consists  of 
those  which  are  intentionally  constructed  by  speculators,  and 
which  contain  some  description  or  indication  distinctive  of  the 
conception  to  which  they  are  applied.  Such  are  a  parallelogram 
(7rapa\\r}\6ypaiJ,fj,ov),  which  denotes  a  plane  figure  bounded  by 
two  pairs  of  parallel  lines ;  a  parallelepiped  (TrapdKKrfKo'jri'jTe^ov), 
which  signifies  a  solid  figure  bounded  by  three  pairs  of  parallel 
planes.  A  triangle  (rplycovos)  and  a  quadrangle  (rerp dycovos) 
were  perhaps  words  invented  independently  of  the  mathemati- 
cians :  but  such  words  extended  to  other  cases,  pentagon,  decagon, 
heccwdecagon,  polygon,  are  inventions  of  scientific  men.  Such 
also  are  tetrahedron,  hexahedron,  dodecahedron,  tesseracontaocto- 
hedron,  polyhedron,  and  the  like.  These  words  being  con- 
structed by  speculative  writers,  explain  themselves,  or  at  least 
require  only  some  conventional  limitation,  easily  adopted.  Thus 
parallelogram  might  mean  a  figure  bounded  by  any  number  of 
sets  of  parallel  lines,  but  it  is  conventionally  restricted  to  a  figure 
of  four  sides.  So  a  great  circle  in  a  sphere  means  one  which 
passes  through  the  centre  of  the  sphere ;  and  a  small  circle  is  any 
other.  So  in  trigonometry,  we  have  the  hypotenuse  (juTrorei- 
vovcra),  or  subtending  line,  to  designate  the  line  subtending  an 
angle.  In  this  branch  of  mathematics  we  have  many  invented 
technical  terms ;  as  complement,  supplement,  cosine,  cotangent,  a 
sphtrical  angle,  the  pole  of  a  circle,  or  of  a  sphere.  The  word  sine 


THE    LANGUAGE    OF    SCIENCE.  Liii 

itself  appears  to  belong  to  the  class  of  terms  already  described  as 
scientific  appropriations  of  common  terms,  although  its  origin  is 
somewhat  obscure. 

Mathematicians  were  naturally  led  to  construct  these  and 
many  other  terms  by  the  progress  of  their  speculations.  In  like 
manner,  when  astronomy  took  the  form  of  a  speculative  science, 
words  were  invented  to  denote  distinctly  the  conceptions  thus  in- 
troduced. Thus  the  sun's  annual  path  among  the  stars,  in  which 
not  only  solar,  but  also  all  lunar  eclipses  occur,  was  termed  the 
ecliptic.  The  circle  which  the  sun  describes  in  his  diurnal  motion, 
when  the  days  and  nights  are  equal,  the  Greeks  called  the  equi- 
diurnal (la-ypepivos,)  the  Latin  astronomers  the  equinoctial,  and 
the  corresponding  circle  on  the  earth  was  the  equator.  The 
ecliptic  intersected  the  equinoctial  in  the  equinoctial  points.  The 
solstices  (in  Greek  rpoTral)  were  the  times  when  the  sun 
arrested  his  motion  northwards  or  southwards  ;  and  the  solstitial 
points  (ra  rpoTriica  o-Tj/Aeia)  were  the  places  in  the  ecliptic 
where  he  then  was.  The  name  of  meridians  was  given  to  circles 
passing  through  the  poles  of  the  equator ;  the  solstitial  colure 
(tco\ovpos,  curtailed),  was  one  of  these  circles  which  passes 
through  the  solstitial  points,  and  is  intercepted  by  the  horizon. 

We  have  borrowed  from  the  Arabians  various  astronomical 
terms,  as  Zenith ,  Nadir,  Azimuth,  Almacantar.  And  these  words, 
which  among  the  Arabians  probably  belonged  to  the  first  class, 
of  appropriated  scientific  terms,  are  for  us  examples  of  the  second 
class,  invented  scientific  terms ;  although  they  differ  from  most 
that  we  have  mentioned,  in  not  containing  an  etymology  corre- 
sponding to  their  meaning  in  any  language  with  which  European 
cultivators  of  science  are  generally  familiar.  Indeed,  the  distinc- 
tion of  our  two  classes,  though  convenient,  is  in  a  great  measure, 
casual.  Thus  most  of  the  words  we  formerly  mentioned,  asparal- 
lax,  horizon,  eclipse,  though  appropriated  technical  terms  among 
the  Greeks,  are  to  us  invented  technical  terms. 

In  the  construction  of  such  terms  as  we  are  now  considering, 
those  languages  have  a  great  advantage  which  possess  a  power  of 
forming  words  by  composition.  This  was  eminently  the  case 
with  the  Greek  language ;  and  hence  most  of  the  ancient  terrm 


L1V  APHORISMS   CONCERNING 

of  science  in  that  language,  when  their  origin  is  once  explained, 
are  clearly  understood  and  easily  retained.  Of  modern  European 
languages,  the  German  possesses  the  greatest  facility  of  com- 
position ;  and  hence  scientific  authors  in  that  language  are 
able  to  invent  terms  which  it  is  impossible  to  imitate  in  the 
other  languages  of  Europe.  Thus  Weiss  distinguishes  his  vari- 
ous systems  of  crystals  as  zwei-und-zwei-gliedrig,  ein-und-zwei- 
gliedrig,  drey-und-drey-gliedrig,  &c.,  (two-and-two-membered, 
one-and-two-membered,  three-and-three-membered.)  And  Hes- 
sel,  also  a  writer  on  crystallography,  speaks  of  doubly-one-mem- 
bered  edges,  four-and-three  spaced  rays,  and  the  like. 

How  far  the  composition  of  words,  in  such  cases,  may  be 
practised  in  the  English  language,  and  the  general  question,  what 
are  the  best  rules  and  artifices  in  such  cases,  I  shall  afterwards 
consider.  In  the  mean  time,  I  may  observe  that  this  list  of  in- 
vented technical  terms  might  easily  be  much  enlarged.  Thus  in 
harmonics  we  have  the  various  intervals,  as  a  Fourth,  a  Fifth,  an 
Octave,  (Diatessaron,  Diapente,  Diapason.)  a  Comma,  which  is  the 
difference  of  a  major  and  minor  Tone ;  we  have  the  various 
Moods  or  Keys,  and  the  notes  of  various  lengths,  as  Minims, 
Breves,  Semibreves,  Quavers.  In  chemistry,  gas  was  at  first  a 
technical  term  invented  by  Van  Helmont,  though  it  has  now 
been  almost  adopted  into  common  language.  I  omit  many 
words  which  will  perhaps  suggest  themselves  to  the  reader, 
because  they  belong  rather  to  the  next  class,  which  I  now  proceed 
to  notice. 

III.  The  third  class  of  technical  terms  consists  of  such  as  are 
constructed  by  men  of  science,  and  involve  some  theoretical  idea 
in  the  meaning  which  their  derivation  implies.  They  do  not 
merely  describe,  like  the  class  last  spoken  of,  but  describe  with 
reference  to  some  doctrine  or  hypothesis  which  is  accepted  as  a 
portion  of  science.  Thus  latitude  and  longitude,  according  to 
their  origin,  signify  breadth  and  length  ;  they  are  used,  however, 
to  denote  measures  of  the  distance  of  a  place  on  the  earth's  sur- 
face from  the  equator,  and  from  the  first  meridian,  of  wThich  dis- 
tances, one  cannot  be  called  length  more  properly  than  the  other. 
But  this  appropriation  of  these  words  may  be  explained  by  recol- 


THE  LANGUAGE  OF  SCIENCE.  LV 

lecting  that  the  earth,  as  known  to  the  ancient  geographers,  was 
much  further  extended  from  east  to  west  than  from  north  to  south. 
The  Precession  of  the  equinoxes  is  a  term  which  implies  that  the 
stars  are  fixed,  while  the  point  which  is  the  origin  of  the  measure 
of  celestial  longitude  moves  backward.    The  Eight  Ascension  of  a 
star  is  a  measure  of  its  position  corresponding  to  terrestrial  longi- 
tude ;  this  quantity  is  identical  with  the  angular  ascent  of  the 
equinoctial  point,  when  the  star  is  in  the  horizon  in  a  right  sphere; 
that  is,  a  sphere  which  supposes  the  spectator  to  be  at  the  equa- 
tor.    The  Oblique  Ascension  (a  term  now  little  used),  is  derived 
in  like  manner  from  an  oblique  sphere.     The  motion  of  a  planet 
is  direct  or  retrograde,  in  consequentia  (signa),  or  in  antecedentia, 
in  reference  to  a  certain  assumed  standard  direction  for  celestial 
motions,  namely,  the  direction  opposite  to  that  of  the  sun's  daily 
motion,  and  agreeing  with  his  annual  motion  among  the  stars ;  or 
with  what  is  much  more  evident,  the  moon's  monthly  motion. 
The  equation  of  time  is  the  quantity  which  must  be  added  to  or 
subtracted  from  the  time  marked  by  the  sun,  in  order  to  reduce 
it  to  a  theoretical  condition  of  equable  progress.     In  like  manner 
the  equation  of  the  centre  of  the  sun  or  of  the  moon  is  the  angle 
which  must  be  added  to,  or  subtracted  from,  the  actual  advance  of 
the  luminary  in  the  heavens,  in  order  to  make  its  motion  equable. 
Besides  the  equation  of  the  centre  of  the  moon,  which  represents 
the  first  and  greatest  of  her  deviations  from  equable  motion,  there 
are  many  other  equations,  by  the  application  of  which  her  motion 
is  brought  nearer  and  nearer  to  perfect  uniformity.     The  second 
of  these  equations  is  called  the  ejection,  the  third  the  variation, 
the  fourth  the  annual  equation.  The  motion  of  the  sun  as  affected 
by  its  inequalities  is  called  his  anomaly,  which  term  denotes  ine- 
quality.    In   the  History  of  Astronomy,  we  find  that  the  ine- 
quable motions  of  the  sun,  moon,  and  planets  were,  in  a  great 
measure,  reduced  to  rule  and  system  by  the  Greeks,  by  the  aid  of 
an  hypothesis  of  circles,  revolving,  and  carrying  in  their  motion 
other  circles  which  also  revolved.     This  hypothesis  introduced 
many  technical  terms,   as  deferent,    epicycle,   eccentric.     In  like 
manner,  the  theories  which  have  more  recently  taken  the  place  of 
the  theory  of  epicycles  have  introduced  other  technical  terms,  as 


LV1  APHORISMS    CONCERNING 

the  elliptical  orbit,  the  radius  vector,  and  the  equable  description 
of  areas  by  this  radius,  which  phrases  express  the  true  laws  of  the 
planetary  motions. 

There  is  no  subject  on  which  theoretical  views  have  been  so 
long  and  so  extensively  prevalent  as  astronomy,  and  therefore  no 
other  science  in  which  there  are  so  many  technical  terms  of 
the  kind  we  are  now  considering.  In  other  subjects,  so  far  as 
theories  have  been  established,  they  have  been  accompanied  by 
the  introduction  or  fixation  of  technical  terms.  Thus,  as  we  have 
seen  in  the  examination  of  the  foundations  of  mechanics,  the 
terms  force  and  inertia  derive  their  precise  meaning  from  a  recog- 
nition of  the  first  law  of  motion ;  accelerating  force  and  compo- 
sition of  motion  involve  the  second  law ;  moving  force,  momentum, 
action  and  reaction,  are  expressions  which  imply  the  third  law. 
The  term  vis  viva  was  introduced  to  express  a  general  property  of 
moving  bodies  ;  and  other  terms  have  been  introduced  for  like  pur- 
poses, as  impetus  by  Smeaton,  and  work  done,  by  other  engineers. 
The  proposition  which  was  termed  the  hydrostatic  paradox  had 
this  name  in  reference  to  its  violating  a  supposed  law  of  the  action 
of  forces.  The  verb  to  gravitate,  and  the  abstract  term  gravitation, 
sealed  the  establishment  of  Newton's  theory  of  the  solar  system. 

In  some  of  the  sciences,  opinions,  either  false  or  disguised  in 
very  fantastical  imagery,  have  prevailed ;  and  the  terms  which 
have  been  introduced  during  the  reign  of  such  opinions,  bear  the 
impress  of  the  time.  Thus  in  the  days  of  alchemy,  the  sub- 
stances with  which  the  operator  dealt  were  personified ;  and  a 
metal  when  exhibited  pure  and  free  from  all  admixture  was  con- 
sidered as  a  little  king,  and  was  hence  called  a  regulus,  a  term 
not  yet  quite  obsolete.  In  like  manner,  a  substance  from  which 
nothing  more  of  any  value  could  be  extracted,  was  dead,  and  was 
called  a  caput  mortuum.  Quick  silver,  that  is,  live  silver  (argen- 
tum  vivum),  was  killed  by  certain  admixtures,  and  was  revived 
when  restored  to  its  pure  state. 

We  find  a  great  number  of  medical  terms  which  bear  the 
mark  of  opinions  formerly  prevalent  among  physicians ;  and 
though  these  opinions  hardly  form  a  part  of  the  progress  of 
science,  and  were  not  presented  in  our  History,  we  may  notice 


THE  LANGUAGE  OF  SCIENCE.  LVl'i 

some  of  these  terms  as  examples  of  the  mode  in  which  words 
involve  in  their  derivation  obsolete  opinions.  Such  words  as 
hysterics,  hypochondriac,  melancholy,  cholera,  colic,  quinsey  (squinan- 
tia,  o-vvdy^rj,  a  suffocation),  megrim,  migraine  (hemicranium,  the 
middle  of  the  skull),  rickets,  (rachitis,  from  £a%W,  the  backbone), 
palsy,  (paralysis,  Trapakvat,?,)  apoplexy  (airoir^ti^ia,  a  stroke), 
emrods  (ai^oppoi^es,  hemorrhoids,  a  flux  of  blood),  imposthume, 
(corrupted  from  aposteme,  airo^^a,  an  abscess),  phthisic  ((f>0cans, 
consumption),  tympany  (rv^avia,  swelling),  dropsy  (hydropsy, 
vSpw-ty),  sciatica,  isciatica  (laxtaSitcrj,  from  tV%/ov,  the  hip), 
catarrh  (tcardppovs,  a  flowing  down),  diarrhoea  (Siappola,  a 
flowing  through),  diabetes  (Biaftr)Trjy,  a  passing  through),  dysentery 
(Svcrevrepia,  a  disorder  of  the  entrails),  arthritic  pains  (from 
apOpa,  the  joints),  are  names  derived  from  the  supposed  or  real 
seat  and  circumstances  of  the  diseases.  The  word  from  which 
the  first  of  the  above  names  is  derived  (vcnepa,  the  last  place,) 
signifies  the  womb,  according  to  its  order  in  a  certain  systematic 
enumeration  of  parts.  The  second  word,  hypochondriac,  means 
something  affecting  the  viscera  below  the  cartilage  of  the  breast- 
bone, which  cartilage  is  called  ^ovSpos ;  melancholy  and  cholera 
derive  their  names  from  supposed  affections  of  %oX^,  the  bile. 
Colic  is  that  which  affects  the  colon  (/cwXov),  the  largest  member 
of  the  bowels.  A  disorder  of  the  eye  is  called  gutta  serena  (the 
"  drop  serene"  of  Milton),  in  contradistinction  to  gutta  turbida, 
in  which  the  impediment  to  vision  is  perceptibly  opake.  Other 
terms  also  record  the  opinions  of  the  ancient  anatomists,  as  duode- 
num, a  certain  portion  of  the  intestines,  which  they  estimated  as 
twelve  inches  long.  We  might  add  other  allusions,  as  the  tendon 
of  Achilles. 

Astrology  also  supplied  a  number  of  words  founded  upon 
fanciful  opinions ;  but  this  study  having  been  expelled  from  the 
list  of  sciences,  such  words  now  survive  only  so  far  as  they  have 
found  a  place  in  common  language.  Thus  men  were  termed  mer- 
curial, martial,  jovial,  or  saturnine,  accordingly  as  their  characters 
were  supposed  to  be  determined  by  the  influence  of  the  planets, 
Mercury,  Mars,  Jupiter,  or  Saturn.  Other  expressions,  such  as 
disastrous,  ill-starred,  exorbitant,  lord  of  the  ascendant,  and  hence 

VOL.  i.  e 


APHORISMS   CONCERNING 

mcenclancy,  influence,  a  sphere  of  aitloji,  and  the  like,  may  serve 
to  show  how  extensively  astrological  opinions  have  affected  lan- 
guage, though  the  doctrine  is  no  longer  a  recognized  science. 

The  preceding  examples  will  make  it  manifest  that  opinions, 
even  of  a  recondite  and  complex  kind,  are  often  implied  in  the 
derivation  of  words ;  and  thus  will  show  how  scientific  terms, 
framed  by  the  cultivators  of  science,  may  involve  received  hypo- 
theses and  theories.  When  terms  are  thus  constructed,  they 
serve  not  only  to  convey  with  ease,  but  to  preserve  steadily  and 
to  diffuse  widely,  the  opinions  which  they  thus  assume.  More- 
over, they  enable  the  speculator  to  employ  these  complex  con- 
ceptions, the  creations  of  science,  and  the  results  of  much  labour 
and  thought,  as  readily  and  familiarly  as  if  they  were  convictions 
borrowed  at  once  from  the  senses.  They  are  thus  powerful 
instruments  in  enabling  philosophers  to  ascend  from  one  step  of 
induction  and  generalization  to  another ;  and  hereby  contribute 
powerfully  to  the  advance  of  knowledge  and  truth. 

It  should  be  noticed,  before  we  proceed,  that  the  names  of 
natural  objects,  when  they  come  to  be  considered  as  the  objects  of 
a  science,  are  selected  according  to  the  processes  already  enume- 
rated. For  the  most  part,  the  natural  historian  adopts  the  com- 
mon names  of  animals,  plants,  minerals,  gems,  and  the  like,  and 
only  endeavours  to  secure  their  steady  and  consistent  application. 
But  many  of  these  names  imply  some  peculiar,  often  fanciful, 
belief  respecting  the  object. 

Various  plants  derive  their  names  from  their  supposed  virtues, 
as  herniaria^  rupture-wort;  or  from  legends,  as  herba  Sancti  Jo- 
kannis,  St.  John's  wort.  The  same  is  the  case  with  minerals : 
thus  the  topaz  was  asserted  to  come  from  an  island  so  shrouded 
in  mists  that  navigators  could  only  conjecture  (roTrd&w)  where  it 
was.  In  these  latter  cases,  however,  the  legend  appears  not  to 
be  the  true  origin  of  the  name,  but  to  be  suggested  by  it. 

The  privilege  of  constructing  names  where  they  are  wranted, 
belongs  to  natural  historians  no  less  than  to  the  cultivators  of 
physical  science ;  yet  in  the  ancient  world,  writers  of  the  former 
class  appear  rarely  to  have  exercised  this  privilege,  even  when 
they  felt  the  imperfections  of  the  current  language.  Thus  Aris- 


THE    LANGUAGE    OF    SCIENCE.  LlX 

totle  repeatedly  mentions  classes  of  animals  which  have  no  name, 
as  co-ordinate  with  classes  that  have  names  ;  but  he  hardly  ven- 
tures to  propose  names  which  may  supply  these  defects*.  The 
vast  importance  of  nomenclature  in  natural  history  was  not  recog- 
nized till  the  modern  period. 

We  have,  however,  hitherto  considered  only  the  formation  or 
appropriation  of  single  terms  in  science ;  except  so  far  as  several 
terms  may  in  some  instances  be  connected  by  reference  to  a  com- 
mon theory.  But  when  the  value  of  technical  terms  began  to  be 
fully  appreciated,  philosophers  proceeded  to  introduce  them  into 
their  sciences  more  copiously  and  in  a  more  systematic  manner. 
In  this  way,  the  modern  history  of  technical  language  has  some 
features  of  a  different  aspect  from  the  ancient ;  and  must  give  rise 
to  a  separate  Aphorism. 

APHORISM  II. 

in  the  Modern  Period  of  Science,  besides  the  three  processes 
anciently  employed  in  the  formation  of  technical  terms,  there 
have  been  introduced  Systematic  Nomenclature,  Systematic 
Terminology,  and  the  Systematic  Modification  of  Terms  to 
express  theoretical  relations-^. 

WRITERS  upon  science  have  gone  on  up  to  modern  times 
forming  such  technical  terms  as  they  had  occasion  for,  by  the 
three  processes  above  described; — namely,  appropriating  and 
limiting  words  in  common  use ; — constructing  for  themselves 
words  descriptive  of  the  conception  which  they  wished  to  con- 
vey  . — or  framing  terms  which  by  their  signification  imply  the 

*  In  his  History  of  Animals,  (book  i.  chap.  6),  he  says  that  the  great 
classes  of  animals  are  Quadrupeds,  Birds,  Fishes,  Whales  (Cetaceans},  Oysters 
(  Testaceans),  animals  like  crabs  which  have  no  general  name  (Crustaceans), 
iL'oft  animals  (Mollusks  and  Insects}.  He  does,  however,  call  the  Crustaces 
by  a  name  (Malacostraca,  soft-shelled)  which  has  since  been  adopted  by 
Naturalists. 

t  On  the  subject  of  Terminology  and  Nomenclature,  see  also  Apho- 
risms Lxxxviii  and  xcviii  concerning  Ideas,  and  book  viii.  chap.  2  of  the 
Philosophy. 

e  2 


LX  APHORISMS   CONCERNING 

adoption  of  a  theory.  Thus  among  the  terms  introduced  by 
the  study  of  the  connexion  between  magnetism  and  electricity, 
the  word  pole  is  an  example  of  the  first  kind ;  the  name  of  the 
subject,  electro-magnetism,  of  the  second ;  and  the  term  current, 
involving  an  hypothesis  of  the  motion  of  a  fluid,  is  an  instance 
of  the  third  class.  In  chemistry,  the  term  salt  was  adopted 
from  common  language,  and  its  meaning  extended  to  denote 
any  compound  of  a  certain  kind;  the  term  neutral  salt  implied 
the  notion  of  a  balanced  opposition  in  the  two  elements  of  the 
compound ;  and  such  words  as  subacid  and  superacid,  invented 
on  purpose,  were  introduced  to  indicate  the  cases  in  which  this 
balance  was  not  attained.  Again,  when  the  phlogistic  theory  of 
chemistry  was  established,  the  term  phlogiston  was  introduced  to 
express  the  theory,  and  from  this  such  terms  as  phlogisticated  and 
dephlogisticated  were  derived,  exclusively  words  of  science.  But 
in  such  instances  as  have  just  been  given,  we  approach  towards  a 
systematic  modification  of  terms,  which  is  a  peculiar  process  of 
modern  times.  Of  this,  modern  chemistry  forms  a  prominent 
example,  which  we  shall  soon  consider,  but  we  shall  first  notice 
the  other  processes  mentioned  in  the  Aphorism. 

I.  In  ancient  times,  no  attempt  was  made  to  invent  or  select 
a  Nomenclature  of  the  objects  of  Natural  History  which  should 
be  precise  and  permanent.  The  omission  of  this  step  by  the 
ancient  naturalists  gave  rise  to  enormous  difficulty  and  loss  of 
time  when  the  sciences  resumed  their  activity.  We  have  seen 
in  the  history  of  the  sciences  of  classification,  and  of  botany  in 
especial*,  that  the  early  cultivators  of  that  study  in  modern  times 
endeavoured  to  identify  all  the  plants  described  by  Greek  and 
Roman  writers  with  those  which  grow  in  the  north  of  Europe ; 
and  were  involved  in  endless  confusion  -J-,  by  the  multiplication 
of  names  of  plants,  at  the  same  time  superfluous  and  ambiguous. 
The  Synonymies  which  botanists  (Bauhin  and  others)  found  it 
necessary  to  publish,  were  the  evidences  of  these  inconveniences. 
In  consequence  of  the  defectiveness  of  the  ancient  botanical 
nomenclature,  we  are  even  yet  uncertain  with  respect  to  the  iden- 

*  Hist.  Ind.  Sci.,  iii.  272.  f  /£.,  293. 


THE   LANGUAGE    OF    SCIENCE  Lxi 

tification  of  some  of  the  most  common  trees  mentioned  by  classical 
writers  *.  The  ignorance  of  botanists  respecting  the  importance  of 
nomenclature  operated  in  another  manner  to  impede  the  progress 
of  science.  As  a  good  nomenclature  presupposes  a  good  system 
of  classification,  so,  on  the  other  hand,  a  system  of  classification 
cannot  become  permanent  without  a  corresponding  nomenclature. 
Csesalpinus,  in  the  sixteenth  century  •(•,  published  an  excellent  sys- 
tem of  arrangement  for  plants ;  but  this,  not  being  connected  with 
any  system  of  names,  was  never  extensively  accepted,  and  soon 
fell  into  oblivion.  The  business  of  framing  a  scientific  botanical 
classification  was  in  this  way  delayed  for  about  a  century.  In 
the  same  manner,  Willoughby's  classification  of  fishes,  though,  as 
Cuvier  says,  far  better  than  any  which  preceded  it,  was  never 
extensively  adopted,  in  consequence  of  having  no  nomenclature 
connected  with  it. 

II.  Probably  one  main  cause  which  so  long  retarded  the  work 
of  fixing  at  the  same  time  the  arrangement  and  the  names  of 
plants,  was  the  great  number  of  minute  and  diversified  particulars 
in  the  structure  of  each  plant  which  such  a  process  implied.  The 
stalks,  leaves,  flowers,  and  fruits  of  vegetables,  with  their  appen- 
dages, may  vary  in  so  many  ways,  that  common  language  is  quite 
insufficient  to  express  clearly  and  precisely  their  resemblances 
and  differences.  Hence  botany  required  not  only  a  fixed  system 
of  names  of  plants,  but  also  an  artificial  system  of  phrases  fitted 
to  describe  their  parts :  not  only  a  Nomenclature,  but  also  a 
Terminology.  The  Terminology  was,  in  fact,  an  instrument  indis- 
pensably requisite  in  giving  fixity  to  the  Nomenclature.  The 
recognition  of  the  kinds  of  plants  must  depend  upon  the  exact 
comparison  of  their  resemblances  and  differences ;  and  to  become 
a  part  of  permanent  science,  this  comparison  must  be  recorded  in 
words. 

The  formation  of  an  exact  descriptive  language  for  botany 
was  thus  the  first  step  in  that  systematic  construction  of  the 
technical  language  of  science,  which  is  one  of  the  main  features 

*  For  instance  whether  the  fagus  of  the  Latins  be  the  beech  or  the 
chesnut. 

t  Hist.  Ind.  Sci.,  iii.  281. 


APHORISMS   CONCERNING 

in  the  intellectual  history  of  modern  times.  The  ancient  botan- 
ists, as  Decandolle*  says,  did  not  make  any  attempt  to  select 
terms  of  which  the  sense  was  rigorously  determined  ;  and  each 
of  them  employed  in  his  descriptions  the  words,  metaphors,  or 
periphrases  which  his  own  genius  suggested.  In  the  History  of 
Botany  f,  I  have  noticed  some  of  the  persons  who  contributed 
to  this  improvement.  "  Chasms,"  it  is  there  stated,  "  first  taught 
botanists  to  describe  well.  He  introduced  exactitude,  precision, 
neatness,  elegance,  method  :  he  says  nothing  superfluous  ;  he 
omits  nothing  necessary."  This  task  was  further  carried  on  by 
Jung  and  RayJ.  In  these  authors  we  see  the  importance  which 
began  to  be  attached  to  the  exact  definition  of  descriptive  terms  ; 
for  example,  Ray  quotes  Jung's  definition  of  Caulis,  a  stalk. 

The  improvement  of  descriptive  language,  and  the  formation 
of  schemes  of  classification  of  plants,  went  on  gradually  for  some 
time,  and  was  much  advanced  by  Tournefort.  But  at  last 
Linnaeus  embodied  and  followed  out  the  convictions  which  had 
gradually  been  accumulating  in  the  breasts  of  botanists  ;  and  by 
remodelling  throughout  both  the  terminology  and  the  nomencla- 
ture of  botany,  produced  one  of  the  greatest  reforms  which  ever 
took  place  in  any  science.  He  thus  supplied  a  conspicuous 
example  of  such  a  reform,  and  a  most  admirable  model  of  a  lan- 
guage, from  which  other  sciences  may  gather  great  instruction. 
I  shall  not  here  give  any  account  of  the  terms  and  words  intro- 
duced by  Linnaeus.  They  have  been  exemplified  in  the  History 
of  Science^  ;  and  the  principles  which  they  involve  I  shall  con- 
sider separately  hereafter.  I  will  only  remind  the  reader  that 
the  great  simplification  in  nomenclature  which  was  the  result  of 
his  labours,  consisted  in  designating  each  kind  of  plant  by  a  binary 
term  consisting  of  the  name  of  the  genus  combined  with  that  of 
the  species  :  an  artifice  seemingly  obvious,  but  more  convenient 
in  its  results  tfran  could  possibly  have  been  anticipated. 

Since  Linnaeus,  the  progress  of  Botanical  Anatomy  and  of 


*  Theor.  £lem.  de  la  Bot.>  p.  327. 

t  Hist.  Ind.  Sci.t  iii.  289.  J  75.,  297  (about  A.D.  1660). 

§  /&.,  307—311. 


THE    LANGUAGE    OF    SCIENCE.  Lxiii 

Descriptive  Botany  have  led  to  the  rejection  of  several  inexact 
expressions,  and  to  the  adoption  of  several  new  terms,  especially 
in  describing  the  structure  of  the  fruit  and  the  parts  of  cryptoga- 
mous  plants.  Hedwig,  Medikus,  Necker,  Desvaux,  Mirbel,  and 
especially  Gsertner,  Link,  and  Richard,  have  proposed  several 
useful  innovations,  in  these  as  in  other  parts  of  the  subject ;  but 
the  general  mass  of  the  words  now  current  consists  still,  and  will 
probably  continue  to  consist,  of  the  terms  established  by  the 
Swedish  Botanist*. 

When  it  was  seen  that  botany  derived  so  great  advantages 
from  a  systematic  improvement  of  its  language,  it  was  natural 
that  other  sciences,  and  especially  classificatory  sciences,  should 
endeavour  to  follow  its  example.  This  attempt  was  made  in 
Mineralogy  by  Werner,  and  afterwards  further  pursued  by  Mohs. 
Werner's  innovations  in  the  descriptive  language  of  Mineralogy 
were  the  result  of  great  acuteness,  an  intimate  acquaintance 
with  minerals,  and  a  most  methodical  spirit:  and  were  in 
most  respects  great  improvements  upon  previous  practices.  Yet 
the  introduction  of  them  into  Mineralogy  was  far  from  rege- 
nerating that  science,  as  Botany  had  been  regenerated  by  the 
Linnsean  reform.  It  would  seem  that  the  perpetual  scrupulous 
attention  to  most  minute  differences,  (as  of  lustre,  colour,  frac- 
ture,) the  greater  part  of  which  are  not  really  important,  fetters 
the  mind,  rather  than  disciplines  or  arms  it  for  generalization. 
Cuvier  has  remarked  -f-  that  Werner,  after  his  first  Essay  on  the 
Characters  of  Minerals,  wrote  little ;  as  if  he  had  been  afraid  of 
using  the  system  which  he  had  created,  and  desirous  of  escaping 
from  the  chains  which  he  had  imposed  upon  others.  And  he 
justly  adds,  that  Werner  dwelt  least,  in  his  descriptions,  upon  that 
which  is  really  the  most  important  feature  of  all,  the  crystalline 
structure.  This,  which  is  truly  a  definite  character,  like  those 
of  Botany,  does,  when  it  can  be  clearly  discerned,  determine  the 
place  of  the  mineral  in  a  system.  This,  therefore,  is  the  character 
which,  of  all  others,  ought  to  be  most  carefully  expressed  by  an 
appropriate  language.  This  task,  hardly  begun  by  Werner,  has 
since  been  fully  executed  by  others,  especially  by  Rome  de  FJsle, 

*  DECANDOLLE,  Th.-Elem.,  p.  307.  t  Elogcs,  ii.  314. 


LX1V  APHORISMS   CONCERNING 

Hauy,  and  Mohs.  All  the  forms  of  crystals  can  be  described 
in  the  most  precise  manner  by  the  aid  of  the  labours  of  these 
writers  and  their  successors.  But  there  is  one  circumstance 
well  worthy  our  notice  in  these  descriptions.  It  is  found  that 
the  language  in  which  they  can  best  be  conveyed  is  not  that  of 
words,  but  of  symbols.  The  relations  of  space  which  are  involved 
in  the  forms  of  crystalline  bodies,  though  perfectly  definite,  are  so 
complex  and  numerous,  that  they  cannot  be  expressed,  except  in 
the  language  of  mathematics :  and  thus  we  have  an  extensive 
and  recondite  branch  of  mathematical  science,  which  is,  in  fact, 
only  a  part  of  the  terminology  of  the  mineralogist. 

The  terminology  of  Mineralogy  being  thus  reformed,  an  at- 
tempt was  made  to  improve  its  nomenclature  also,  by  following  the 
example  of  Botany.  Professor  Mohs  was  the  proposer  of  this 
innovation.  The  names  framed  by  him  were,  however,  not  com- 
posed of  two  but  of  three  elements,  designating  respectively  the 
Species,  the  Genus,  and  the  Order*:  thus  he  has  such  species  as 
RJiombohedral  Lime  Haloide,  Octahedral  Fluor  Haloide,  Prismatic 
Hal  Baryte.  These  names  have  not  been  generally  adopted  ;  nor 
is  it  likely  that  any  names  constructed  on  such  a  scheme  will  find 
acceptance  among  mineralogists,  till  the  higher  divisions  of  the 
system  are  found  to  have  some  definite  character.  We  see  no 
real  mineralogical  significance  in  Mohs's  Genera  and  Orders,  and 
hence  we  do  not  expect  them  to  retain  a  permanent  place  in 
the  science. 

The  only  systematic  names  which  have  hitherto  been  generally 
admitted  in  Mineralogy,  are  those  expressing  the  chemical  consti- 
tution of  the  substance  ;  and  these  belong  to  a  system  of  technical 
terms  different  from  any  we  have  yet  spoken  of,  namely  to  terms 
formed  by  systematic  modification. 

III.  The  language  of  Chemistry  was  already,  as  we  have  seen, 
tending  to  assume  a  systematic  character,  even  under  the  reign  of 
the  phlogiston  theory.  But  when  the  oxygen  theory  succeeded  to 
the  throne,  it  very  fortunately  happened  that  its  supporters  had  the 
courage  and  the  foresight  to  undertake  a  completely  new  and  sys- 
tematic recoinage  of  the  terms  belonging  to  the  science.  The  new 
*  Hist.  Ind.  Sci.,  iii.  240. 


THE  LANGUAGE  OF  SCIENCE.  LXV 

nomenclature  \vas  constructed  upon  a  principle  hitherto  hardly 
applied  in  science,  but  eminently  commodious  and  fertile ;  namely, 
the  principle  of  indicating  a  modification  of  relations  of  elements, 
by  a  change  in  the  termination  of  the  word.  Thus  the  new  che- 
mical school  spoke  of  sulphuric  and  sulphurous  acids  ;  of  sulphates 
and  sulphites  of  bases  ;  and  of  sulphurets  of  metals  ;  and  in  like 
manner,  of  phosphoric  and  phosphorous  acids,  of  phosphates,  phos- 
phites, phosphurets.  In  this  manner  a  nomenclature  was  produced, 
in  which  the  very  name  of  a  substance  indicated  at  once  its  con- 
stitution and  place  in  the  system. 

The  introduction  of  this  chemical  language  can  never  cease  to 
be  considered  one  of  the  most  important  steps  ever  made  in  the 
improvement  of  technical  terms ;  and  as  a  signal  instance  of  the 
advantages  which  may  result  from  artifices  apparently  trivial,  if 
employed  in  a  manner  conformable  to  the  laws  of  phenomena,  and 
systematically  pursued.  It  was,  however,  proved  that  this  lan- 
guage, with  all  its  merits,  had  some  defects.  The  relations  of 
elements  in  composition  were  discovered  to  be  more  numerous 
than  the  modes  of  expression  which  the  terminations  supplied. 
Besides  the  sulphurous  and  sulphuric  acids,  it  appeared  there  were 
others  ;  these  were  called  the  hyposulphurous  and  hyposulphuric : 
but  these  names,  though  convenient,  no  longer  implied,  by  their 
form,  any  definite  relation.  The  compounds  of  Nitrogen  and 
Oxygen  are,  in  order,  the  Protoxide,  the  Deutoxide  or  Binoxide; 
Hyponitrous  Acid,  Nitrous  Acid,  and  Nitric  Acid.  The  nomen- 
clature here  ceases  to  be  systematic.  We  have  three  oxides  of 
Iron,  of  which  we  may  call  the  first  the  Protoxide,  but  we  cannot 
call  the  others  the  Deutoxide  and  Tritoxide,  for  by  doing  so  we 
should  convey  a  perfectly  erroneous  notion  of  the  proportions  of 
the  elements.  They  are  called  the  Protoxide,  the  Black  Oxide, 
and  the  Peroxide.  We  are  here  thrown  back  upon  terms  quite 
unconnected  with  the  system. 

Other  defects  in  the  nomenclature  arose  from  errors  in  the 
theory  ;  as  for  example  the  names  of  the  muriatic,  oxymuriatic, 
and  hyperoxymuriatic  acids ;  which,  after  the  establishment  of  the 
new  theory  of  chlorine,  were  changed  to  hydrochloric  acid,  chlo- 
rine, and  chloric  acid. 


LXVi  APHORISMS  CONCERNING 

Thus  the  chemical  system  of  nomenclature,  founded  upon  the 
oxygen  theory,  while  it  shows  how  much  may  he  effected  by  a 
good  and  consistent  scheme  of  terms,  framed  according  to  the  real 
relations  of  objects,  proves  also  that  such  a  scheme  can  hardly  be 
permanent  in  its  original  form,  bnt  will  almost  inevitably  become 
imperfect  and  anomalous,  in  consequence  of  the  accumulation  of 
new  facts,  and  the  introduction  of  new  generalizations.  Still, 
we  may  venture  to  say  that  such  a  scheme  does  not,  on  this 
account,  become  worthless  ;  for  it  not  only  answers  its  purpose 
in  the  stage  of  scientific  progress  to  which  it  belongs  : — so  far 
as  it  is  not  erroneous,  or  merely  conventional,  but  really  sys- 
tematic and  significant  of  truth,  its  terms  can  be  translated  at 
once  into  the  language  of  any  higher  generalization  which  is  after- 
wards arrived  at.  If  terms  express  relations  really  ascertained  to 
be  true,  they  can  never  lose  their  value  by  any  change  of  the 
received  theory.  They  are  like  coins  of  pure  metal,  which,  even 
when  carried  into  a  country  which  does  not  recognize  the  sove- 
reign whose  impress  they  bear,  are  still  gladly  received,  and  may, 
by  the  addition  of  an  explanatory  mark,  continue  part  of  the 
common  currency  of  the  country. 

These  two  great  instances  of  the  reform  of  scientific  language, 
in  Botany  and  in  Chemistry,  are  much  the  most  important  and 
instructive  events  of  this  kind  which  the  history  of  science  offers. 
It  is  not  necessary  to  pursue  our  historical  survey  further.  Our 
remaining  Aphorisms  respecting  the  Language  of  Science  will  be 
collected  and  illustrated  indiscriminately,  from  the  precepts  and 
the  'examples  of  preceding  philosophers  of  all  periods. 

We  may,  however,  remark  that  Aphorisms  III.,  IV.,  V., 
VI.,  VII.,  respect  peculiarly  the  Formation  of  Technical  Terms 
by  the  Appropriation  of  Common  Words,  while  the  remaining 
ones  apply  to  the  Formation  of  New  Terms. 

It  does  not  appear  possible  to  lay  down  a  system  of  rules 
which  may  determine  and  regulate  the  construction  of  all  techni- 
cal terms,  on  all  the  occasions  on  which  the  progress  of  science 
makes  them  necessary  or  convenient.  But  if  we  can  collect  a  few 
maxims  such  as  have  already  offered  themselves  to  the  minds  of 
philosophers,  or  such  as  may  be  justified  by  the  instances  by  which 


THE  LANGUAGE  OF  SCIENCE.  LXV11 

we  shall  illustrate  them,  these  maxims  may  avail  to  guide  us  in 
doubtful  cases,  and  to  prevent  our  aiming  at  advantages  which  arc 
unattainable,  or  being  disturbed  by  seeming  imperfections  which 
are  really  no  evils.  I  shall  therefore  state  such  maxims  of  this 
kind  as  seem  most  sound  and  useful. 

APHORISM  III. 

In  framing   scientific  terms,  the  appropriation  of  old  words    is 
preferable  to  the  invention  of  new  ones. 

This  maxim  is  stated  by  Bacon  in  his  usual  striking  man- 
ner. After  mentioning  Metaphysic^  as  one  of  the  divisions  of 
Natural  Philosophy,  he  adds*:  "Wherein  I  desire  it  may  be 
conceived  that  I  use  the  word  metaphysic  in  a  differing  sense 
from  that  that  is  received :  and  in  like  manner  I  doubt  not  but 
it  will  easily  appear  to  men  of  judgment  that  in  this  and  other 
particulars,  wheresoever  my  conception  and  notion  may  differ 
from  the  ancient,  yet  I  am  studious  to  keep  the  ancient  terms. 
For,  hoping  well  to  deliver  myself  from  mistaking  by  the  order 
and  perspicuous  expressing  of  that  I  do  propound  ;  I  am  otherwise 
zealous  and  affectionate  to  recede  as  little  from  antiquity,  either  in 
terms  or  opinions,  as  may  stand  with  truth,  and  the  proficience  of 
knowledge.  ...  To  me,  that  do  desire,  as  much  as  lieth  in  my 
pen,  to  ground  a  sociable  intercourse  between  antiquity  and  pro- 
ficience, it  seemeth  best  to  keep  a  way  with  antiquity  usque  ad 
aras ;  and  therefore  to  retain  [the  ancient  terms,  though  I  some- 
times alter  the  uses  and  definitions  ;  according  to  the  moderate 
proceeding  in  civil  governments,  when,  although  there  be  some 
alteration,  yet  that  holdetk  which  Tacitus  wisely  noteth,  eadem 
magistratuum  vocdbula" 

We  have  had  before  us  a  sufficient  number  of  examples  of 
scientific  terms  thus  framed  ;  for  they  formed  the  first  of  three 
classes  which  we  described  in  the  First  Aphorism.  And  we 
may  again  remark,  that  science,  when  she  thus  adopts  terms 
which  are  in  common  use,  always  limits  and  fixes  their  meaning 
in  a  technical  manner.  We  may  also  repeat  here  the  warning 
*  De  Augm.y  Lib.  iii.  c.  4. 


LXV111  APHORISMS  CONCERNING 

already  given  respecting  terms  of  this  kind,  that  they  are  peculi- 
arly liable  to  mislead  readers  who  do  not  take  care  to  understand 
them  in  their  technical  instead  of  their  common  signification. 
Force,  momentum,  inertia,  impetus,  vis  viva,  are  terms  which  are 
very  useful,  if  we  rigorously  bear  in  mind  the  import  which  belongs 
to  each  of  them  in  the  best  treatises  on  Mechanics ;  but  if  the 
reader  content  himself  with  conjecturing  their  meaning  from  the 
context,  his  knowledge  will  be  confused  and  worthless. 

In  the  application  of  this  Third  Aphorism,  other  rules  are 
to  be  attended  to,  which  I  add. 

APHORISM  IV. 

When  common  words  are  appropriated  as  technical  terms,  their 
meaning  and  relations  in  common  use  should  be  retained  as  far 
as  can  conveniently  be  done. 

I  WILL  state  an  example  in  which  this  rule  seems  to  be  appli- 
cable. Mr.  Davies  Gilbert*  has  recently  proposed  the  term 
efficiency  to  designate  the  work  which  a  machine,  according  to 
the  force  exerted  upon  it,  is  capable  of  doing ;  the  work  being 
measured  by  the  weight  raised,  and  the  space  through  which  it 
is  raised,  jointly.  The  usual  term  employed  among  engineers  for 
the  work  which  a  machine  actually  does,  measured  in  the  way 
just  stated,  is  duty.  But  as  there  appears  to  be  a  little  incon- 
gruity in  calling  that  work  efficiency  which  the  machine  ought  to 
do,  when  we  call  that  work  duty  which  it  really  does,  I  have 
proposed  to  term  these  two  quantities  theoretical  efficiency  and 
practical  efficiency,  or  theoretical  duty  and  practical  duty. 

Since  common  words  are  often  vague  in  their  meaning,  I 
add  as  a  necessary  accompaniment  to  the  Third  Aphorism  the 
following : — 

*  Phil  Trans.  1827,  p.  25. 


THE  LANGUAGE  OF  SCIENCE.  LXlX 

APHORISM  Y. 

When  common  words  are  appropriated  as  technical  terms,  their 
meaning  may  be  modified,  and  must  be  rigorously  fixed. 

THIS  is  stated  by  Bacon  in  the  above  extract :  "to  retain  the 
ancient  terms,  though  I  sometimes  alter  the  uses  and  definitions" 
The  scientific  use  of  the  term  is  in  all  cases  much  more  precise 
than  the  common  use.  The  loose  notions  of  velocity  and  force 
for  instance,  which  are  sufficient  for  the  usual  purposes  of  lan- 
guage, require  to  be  fixed  by  exact  measures  when  these  are  made 
terms  in  the  science  of  Mechanics. 

This  scientific  fixation  of  the  meaning  of  words  is  to  be  looked 
upon  as  a  matter  of  convention,  although  it  is  in  reality  often  an 
inevitable  result  of  the  progress  of  science.  Momentum  is  con- 
ventionally defined  to  be  the  product  of  the  -numbers  expressing 
the  weight  and  the  velocity ;  but  then,  it  could  be  of  no  use 
in  expressing  the  laws  of  motion  if  it  were  defined  otherwise. 

Hence  it  is  no  valid  objection  to  a  scientific  term  that  the 
word  in  common  language  does  not  mean  exactly  the  same  as 
in  its  common  use.  It  is  no  sufficient  reason  against  the  use  of 
the  term  acid  for  a  class  of  bodies,  that  all  the  substances  belong- 
ing to  this  class  are  not  sour.  We  have  seen  that  a  trapezium  is 
used  in  geometry  for  any  four-sided  figure,  though  originally  it 
meant  a  figure  with  two  opposite  sides  parallel  and  the  two  others 
equal.  A  certain  stratum  which  lies  below  the  chalk  is  termed 
by  English  geologists  the  green  sand.  It  has  sometimes  been 
objected  to  this  denomination,  that  the  stratum  has  very  fre- 
quently no  tinge  of  green,  and  that  it  is  often  composed  of  lime 
with  little  or  no  sand.  Yet  the  term  is  a  good  technical  term 
in  spite  of  these  apparent  improprieties ;  so  long  as  it  is  care- 
fully applied  to  that  stratum  which  is  geologically  equivalent  to 
the  greenish  sandy  bed  to  which  the  appellation  was  originally 
applied. 

When  it  appeared  that  geometry  would  have  to  be  employed 
as  much  at  least  about  the  heavens  as  the  earth,  Plato  exclaimed 
against  the  folly  of  calling  the  science  by  such  a  name ;  since  the 
word  signifies  "  earth-measuring ;"  yet  the  word  geometry  has 


LXX  APHORISMS  CONCERNING 

retained  its  place  and  answered  its  purpose  perfectly  welljip  to 
the  present  day. 

But  though  the  meaning  of  the  term  may  be  modified  or 
extended,  it  must  be  rigorously  fixed  when  it  is  appropriated  to 
science.  This  process  is  most  abundantly  exemplified  by  the 
terminology  of  Natural  History,  and  especially  of  Botany,  in 
which  each  term  has  a  most  precise  meaning  assigned  to  it. 
Thus  Linnaeus  established  exact  distinctions  between  fasciculus, 
capitulum,  racemus,  thyrsus,  paniculus,  spica,  amentum,  corymbus, 
umbella,  cyma,  verticillus ;  or,  in  the  language  of  English  Bo- 
tanists, a  tuft,  a  head,  a  duster,  a  bunch,  a  panicle,  a  spike,  a  cat- 
kin, a  corymb,  an  umbel,  a  cyme,  a  whorl.  And  it  has  since  been 
laid  down  as  a  rule*,  that  each  organ  ought  to  have  a  separate  and 
appropriate  name ;  so  that  the  term  leaf,  for  instance,  shall  never 
be  applied  to  a  leaflet,  a  bractea,  or  a  sepal  of  the  calyx. 

Botanists  have  not  been  content  with  fixing  the  meaning  of 
their  terms  by  verbal  definition,  but  have  also  illustrated  them 
by  figures,  which  address  the  eye.  Of  these,  as  excellent  modern 
examples,  may  be  mentioned  those  which  occur  in  the  works  of 
Mirbelf,  and  LmdleyJ. 

APHORISM  VI. 

When  common  words  are  appropriated  as  technical  terms,  this  must 
be  done  so  that  they  are  not  ambiguous  in  their  application. 

AN  example  will  explain  this  maxim.  The  conditions  of  a 
body,  as  a  solid,  a  liquid,  and  an  air,  have  been  distinguished  as 
different  forms  of  the  body.  But  the  word  form,  as  applied  to 
bodies,  has  other  meanings ;  so  that  if  we  were  to  inquire  in  what 
form  water  exists  in  a  snow-cloud,  it  might  be  doubted  whether 
the  forms  of  crystallization  were  meant,  or  the  different  forms  of 
ice,  water,  and  vapour.  Hence  I  have  proposed§  to  reject  the 
term  form  in  such  cases,  and  to  speak  of  the  different  consistence 
of  a  body  in  these  conditions.  The  term  consistence  is  usually 
applied  to  conditions  between  solid  and  fluid ;  and  may  without 

*  DECANDOLLE,  Theor.  EL,  328.  t  Elemens  de  Botanique. 

J  Elements  of  Botany.  §  Hist.  Ind.  Sci.9  iii. 


THE  LANGUAGE  OF  SCIENCE.  LXXi 

effort  be  extended  to  those  limiting  conditions.  And  though  it 
may  appear  more  harsh  to  extend  the  term  consistence  to  the 
state  of  air,  it  may  be  justified  by  what  has  been  said  in  speaking 
of  Aphorism  V. 

I  may  notice  another  example  of  the  necessity  of  avoiding 
ambiguous  words.  A  philosopher  who  makes  method  his  study, 
would  naturally  be  termed  a  methodist ;  but  unluckily  this  word 
is  already  appropriated  to  a  religious  sect :  and  hence  we  could 
hardly  venture  to  speak  of  Csesalpinus,  Ray,  Morison,  Rivinus, 
Tournefort,  Linnaeus,  and  their  successors,  as  botanical  methodists» 
Again,  by  this  maxim,  we  are  almost  debarred  from  using  the 
term  physician  for  a  cultivator  of  the  science  of  physics,  because 
it  already  signifies  a  practiser  of  physic.  We  might,  perhaps* 
still  use  physician  as  the  equivalent  of  the  French  physicien, 
in  virtue  of  Aphorism  V.;  but  probably  it  would  be  better  to 
form  a  new  word.  Thus  we  may  say,  that  while  the  Naturalist 
employs  principally  the  ideas  of  resemblance  and  life,  the  Physicist 
proceeds  upon  the  ideas  of  force,  matter,  and  the  properties  of 
matter. 

Whatever  may  be  thought  of  this  proposal,  the  maxim  which 
it  implies  is  frequently  useful.  It  is  this. 

APHORISM  VII. 

It  is  better  to  form  new  words  as  technical  terms,  than  to  employ 
old  ones  in  which  the  last  three  Aphorisms  cannot  be  complied 
with. 

THE  principal  inconvenience  attending  the  employment  of 
new  words  constructed  expressly  for  the  use  of  science,  is  the 
difficulty  of  effectually  introducing  them.  Readers  will  not 
readily  take  the  trouble  to  learn  the  meaning  of  a  word,  in  which 
the  memory  is  not  assisted  by  some  obvious  suggestion  connected 
with  the  common  use  of  language.  When  this  difficulty  is 
overcome,  the  new  word  is  better  than  one  merely  appropriated ; 
since  it  is  more  secure  from  vagueness  and  confusion.  And  in 
cases  where  the  inconveniences  belonging  to  a  scientific  use  of 
common  words  become  great  and  inevitable,  a  new  word  must 
be  framed  and  introduced. 


LXX11  APHORISMS  CONCERNING 

The  Maxims  which  belong  to  the  construction  of  such  words 
will  be  stated  hereafter ;  but  I  may  notice  an  instance  or  two 
tending  to  show  the  necessity  of  the  Maxim  now  before  us. 

The  word  Force  has  been  appropriated  in  the  science  of 
Mechanics  in  two  senses  :  as  indicating  the  cause  of  motion  ;  and 
again,  as  expressing  certain  measures  of  the  effects  of  this  cause, 
in  the  phrases  accelerating  force  and  moving  force.  Hence  we 
might  have  occasion  to  speak  of  the  accelerating  or  moving  force 
of  a  certain  force ;  for  instance,  if  we  were  to  say  that  the  centre 
of  force  which  governs  the  motions  of  the  planets  resides  in  the 
sun  ;  and  that  the  accelerating  force  of  this  force  varies  only  with 
the  distance,  but  its  moving  force  varies  as  the  product  of  the 
mass  of  the  sun  and  the  planet.  This  is  a  harsh  and  incongruous 
mode  of  expression ;  and  might  have  been  avoided,  if,  instead  of 
accelerating  force  and  moving  force,  single  abstract  terms  had  been 
introduced  by  Newton :  if,  for  instance,  he  had  said  that  the 
velocity  generated  in  a  second  measures  the  acceleratimty  of  the 
force  which  produces  it,  and  the  momentum  produced  in  a  second 
measures  the  motimty  of  the  force. 

The  science  which  treats  of  heat  has  hitherto  had  no  special 
designation  :  treatises  upon  it  have  generally  been  termed  treatises 
On  Heat.  But  this  practice  of  employing  the  same  term  to  denote 
the  property  and  the  science  which  treats  of  it,  is  awkward  and 
often  ambiguous.  And  it  is  further  attended  with  this  incon- 
venience, that  we  have  no  adjective  derived  from  the  name  of  the 
science,  as  we  have  in  other  cases,  when  we  speak  of  acoustical 
experiments  and  optical  theories.  This  inconvenience  has  led 
various  persons  to  suggest  names  for  the  Science  of  Heat.  M. 
Le  Comte  terms  it  Thermology.  In  the  History  of  the  Sciences, 
I  have  named  it  Thermotics,  which  appears  to  me  to  agree  better 
with  the  analogy  of  the  names  of  other  corresponding  sciences, 
Acoustics  and  Optics. 

Electricity  is  in  the  same  condition  as  heat ;  having  only  one 
word  to  express  the  property  and  the  science.  M.  Le  Comte 
proposes  Electrology :  for  the  same  reason  as  before,  I  should 
conceive  Electrics  more  agreeable  to  analogy.  The  coincidence 
of  the  word  with  the  plural  of  Electric  would  not  give  rise  to 


THE  LANGUAGE  OF  SCIENCE.  LXX111 

ambiguity ;  for  Electrics ',  taken  as  the  name  of  a  science,  would 
be  singular,  like  Optics  and  Mechanics.  But  a  term  offers  itself 
to  express  common  or  machine  Electrics,  which  appears  worthy 
of  admission,  though  involving  a  theoretical  view.  The  received 
doctrine  of  the  difference  between  voltaic  and  common  electricity 
is,  that  in  the  former  case  the  fluid  must  be  considered  as  in 
motion,  in  the  latter  as  at  rest.  The  science  which  treats  of  the 
former  class  of  subjects  is  commonly  termed  Electrodynamics, 
which  obviously  suggests  the  name  Electrostatics  for  the  latter. 

The  subject  of  the  Tides  is,  in  like  manner,  destitute  of  any 
name  which  designates  the  science  concerned  about  it.  I  have 
ventured  to  employ  the  term  Tidology,  having  been  much  engaged 
in  tidological  researches. 

Many  persons  possess  a  peculiarity  of  vision,  which  disables 
them  from  distinguishing  certain  colours.  On  examining  many 
such  cases,  we  find  that  in  all  such  persons  the  peculiarities  are 
the  same ;  all  of  them  confounding  scarlet  with  green,  and  pink 
with  blue.  Hence  they  form  a  class,  which,  for  the  convenience 
of  physiologists  and  others,  ought  to  have  a  fixed  designation. 
Instead  of  calling  them,  as  has  usually  been  done,  "persons  having 
a  peculiarity  of  vision,"  we  might  take  a  Greek  term  implying 
this  meaning,  and  term  them  Idiopts. 

But  my  business  at  present  is  not  to  speak  of  the  selection  of 
new  terms  when  they  are  introduced,  but  to  illustrate  the  maxim 
that  the  necessity  for  their  introduction  often  arises.  The  con- 
struction of  new  terms  will  be  treated  of  subsequently. 


APHORISM  VIII. 

Terms  must  be  constructed  and  appropriated  so  as  to  be  fitted  to 
enunciate  simply  and  clearly  true  general  propositions. 

THIS  Aphorism  may  be  considered  as  the  fundamental  prin- 
ciple and  supreme  rule  of  all  scientific  terminology.  It  is  asserted 
by  Cuvier,  speaking  of  a  particular  case.  Thus  he  says*  of 

*  Regne  Animal,  Introd.  viii. 
VOL.  I.  / 


LXXiv  APHORISMS  CONCERNING 

Gmelin,  that  by  placing  the  lamantin  in  the  genus  of  morses,  and 
the  siren  in  the  genus  of  eels,  he  had  rendered  every  general  pro- 
position respecting  the  organization  of  those  genera  impossible. 

The  maxim  is  true  of  words  appropriated  as  well  as  invented, 
and  applies  equally  to  the  mathematical,  chemical,  and  classifi- 
catory  sciences.  With  regard  to  most  of  these,  and  especially  the 
two  former  classes,  it  has  been  abundantly  exemplified  already,  in 
what  has  previously  been  said,  and  in  the  History  of  the  Sciences. 
For  we  have  there  had  to  notice  many  technical  terms,  with  the 
occasions  of  their  introduction  ;  and  all  these  occasions  have 
involved  the  intention  of  expressing  in  a  convenient  manner  some 
truth  or  supposed  truth.  The  terms  of  Astronomy  were  adopted 
for  the  purpose  of  stating  and  reasoning  upon  the  relations  of  the 
celestial  motions,  according  to  the  doctrine  of  the  sphere,  and  the 
other  laws  which  were  discovered  by  astronomers.  The  few 
technical  terms  which  belong  to  Mechanics,  force,  velocity,  mo- 
mentum, inertia,  See.,  were  employed  from  the  first  with  a  view 
to  the  expression  of  the  laws  of  motion  and  of  rest ;  and  were,  in 
the  end,  limited  so  as  truly  and  simply  to  express  those  laws  when 
they  were  fully  ascertained.  In  Chemistry,  the  term  phlogiston 
was  useful,  as  has  been  shown  in  the  History,  in  classing  toge- 
ther processes  which  really  are  of  the  same  nature ;  and  the 
nomenclature  of  the  oxygen  theory  was  still  preferable,  because  it 
enabled  the  chemist  to  express  a  still  greater  number  of  general 
truths. 

To  the  connexion  here  asserted,  of  theory  and  nomenclature, 
we  have  the  testimony  of  the  author  of  the  oxygen  theory.  In 
the  Preface  to  his  Chemistry,  Lavoisier  says : — "  Thus  while  I 
thought  myself  employed  only  in  forming  a  Nomenclature,  and 
while  I  proposed  to  myself  nothing  more  than  to  improve  the 
chemical  language,  my  work  transformed  itself  by  degrees,  with- 
out my  being  able  to  prevent  it,  into  a  Treatise  on  the  Elements 
of  Chemistry.11  And  he  then  proceeds  to  show  how  this  hap- 
pened. 

It  is,  however,  mainly  through  the  progress  of  Natural  History 
in  modern  times,  that  philosophers  have  been  led  to  see  the  import- 
ance and  necessity  of  new  terms  in  expressing  new  truths.  Thus 


THE  LANGUAGE  OF  SCIENCE.  LXXY 

Harvey,  in  the  Preface  to  his  work  on  Generation,  says : — "  Be 
not  offended  if  in  setting  out  the  History  of  the  Egg  I  make  use 
of  a  new  method,  and  sometimes  of  unusual  terms.  For  as  they 
which  find  out  a  new  plantation  and  new  shores  call  them  by 
names  of  their  own  coining,  which  posterity  afterwards  accepts 
and  receives,  so  those  that  find  out  new  secrets  have  good  title  to 
their  compellation.  And  here,  methinks,  I  hear  Galen  advising: 
If  we  consent  in  the  things,  contend  not  about  the  words." 

The  Nomenclature  which  answers  the  purposes  of  Natural 
History  is  a  systematic  nomenclature,  and  will  be  further  consi- 
dered under  the  next  Aphorism.  But  we  may  remark,  that  the 
Aphorism  now  before  us  governs  the  use  of  words,  not  in  science 
only,  but  in  common  language  also.  Are  we  to  apply  the  name 
fish  to  animals  of  the  whale  kind  I  The  answer  is  determined  by 
our  present  rule :  we  are  to  do  so,  or  not,  accordingly  as  we  can 
best  express  true  propositions.  If  we  are  speaking  of  the  internal 
structure  and  physiology  of  the  animal,  we  must  not  call  them 
fish  ;  for  in  these  respects  they  deviate  widely  from  fishes :  they 
have  warm  blood,  and  produce  and  suckle  their  young  as  land 
quadrupeds  do.  But  this  would  not  prevent  our  speaking  of  the 
whale-fishery,  and  calling  such  animals  fish  on  all  occasion  con- 
nected with  this  employment;  for  the  relations  thus  arising  depend 
upon  the  animal's  living  in  the  water,  and  being  caught  in  a 
manner  similar  to  other  fishes.  A  plea  that  human  laws  which 
mention  fish  do  not  apply  to  whales,  would  be  rejected  at  once  by 
an  intelligent  judge. 


APHORISM  IX. 

In  the  Classifcatory  Sciences,  a  systematic  Nomenclature  is  neces- 
sary ;  and  the  System  and  the  Nomenclature  are  each  essential 
to  the  utility  of  the  other. 

THE  inconveniences  arising  from  the  want  of  a  good  Nomen- 
clature were  long  felt  in  Botany,  and  are  still  felt  in  Mineralogy. 
The  attempts  to  remedy  them  by  Synonymies  are  very  ineffective, 


LXXV1  APHORISMS   CONCERNING 

for  such  comparisons  of  synonymes  do  not  supply  a  systematic  no- 
menclature ;  and  such  a  one  alone  can  enable  us  to  state  general 
truths  respecting  the  objects  of  which  the  classificatory  sciences 
treat.  The  system  and  the  names  ought  to  be  introduced  together ; 
for  the  former  is  a  collection  of  asserted  analogies  and  resem- 
blances, for  which  the  latter  provide  simple  and  permanent  ex- 
pressions. Hence  it  has  repeatedly  occurred  in  the  progress  of 
Natural  History,  that  good  systems  did  not  take  root,  or  produce 
any  lasting  effect  among  naturalists,  because  they  were  not  accom- 
panied by  a  corresponding  nomenclature.  In  this  way,  as  we  have 
already  noticed,  the  excellent  botanical  system  of  Csesalpinus  was 
without  immediate  effect  upon  the  science.  The  work  of  Wil- 
loughby,  as  Cuvier  says*,  forms  an  epoch,  and  a  happy  epoch  in 
Ichthyology ;  yet  because  Willoughby  had  no  nomenclature  of  his 
own,  and  no  fixed  names  for  his  genera,  his  immediate  influence 
was  not  great.  Again,  in  speaking  of  Schlotheini's  work  con- 
taining representations  of  fossil  vegetables,  M.  Adolphe  Brong- 
niart  observes -f-  that  the  figures  and  descriptions  are  so  good,  that 
if  the  author  had  established  a  nomenclature  for  the  objects  he 
describes,  his  work  would  have  become  the  basis  of  all  succeeding 
labours  on  the  same  subject. 

As  additional  examples  of  cases  in  which  the  improvement  of 
classification,  in  recent  times,  has  led  philosophers  to  propose  new 
names,  I  may  mention  the  term  Pcecilite,  proposed  by  Mr.  Cony- 
beare  to  designate  the  group  of  strata  which  lies  below  the  oolites 
and  lias,  including  the  new  red  or  variegated  sandstone,  with  the 
keuper  above,  and  the  magnesian  limestone  below  it.  Again,  the 
transition  districts  of  our  island  have  recently  been  reduced  to 
system  by  Professor  Sedgwick  and  Mr.  Murchison  ;  and  this  step 
has  been  marked  by  the  terms  Cambrian  system,  and  Silurian 
system,  applied  to  the  two  great  groups  of  formations  which  they 
have  respectively  examined,  and  by  several  other  names  of  the 
subordinate  members  of  these  formations. 

Thus  system  and  nomenclature  are  each  essential  to  the  other. 
Without  nomenclature,  the  system  is  not  permanently  incor- 

*  Hist,  dcs  Poissons,  Pref.  t  Prjdrom.  Veg.  Foss.,  p.  3. 


THE  LANGUAGE  OF  SCIENCE.  LXXvii 

porated  into  the  general  body  of  knowledge,  and  made  an 
instrument  of  future  progress.  Without  system,  the  names  can- 
not express  general  truths,  and  contain  no  reason  why  they  should 
he  employed  in  preference  to  any  other  names. 

This  has  been  generally  acknowledged  by  the  most  philosophi- 
cal naturalists  of  modern  times.  Thus  Linnaeus  begins  that  part 
of  his  Botanical  Philosophy  in  which  Names  are  treated  of,  by 
stating  that  the  foundation  of  botany  is  twofold,  Disposition  and 
Denomination  ;  and  he  adds  this  Latin  line, 

Nomina  si  nescis  perit  et  cognitio  remm. 

And  Cuvier,  in  the  Preface  to  his  Animal  Kingdom,  explains,  in 
a  very  striking  manner,  how  the  attempt  to  connect  zoology  with 
anatomy  led  him,  at  the  same  time,  to  reform  the  classifications, 
and  to  correct  the  nomenclature  of  preceding  zoologists. 

I  have  stated  that  in  mineralogy  we  are  still  destitute  of  a 
good  nomenclature  generally  current.  From  what  has  now  been 
said,  it  will  be  seen  that  it  may  be  very  far  from  easy  to  supply 
this  defect,  since  we  have,  as  yet,  no  generally  received  system 
of  mineralogical  classification.  Till  we  know  what  are  really 
different  species  of  minerals,  and  in  what  larger  groups  these  spe- 
cies can  be  arranged,  so  as  to  have  common  properties,  we  shall 
never  obtain  a  permanent  mineralogical  nomenclature.  Thus 
Leucocydite  and  Tesselite  are  minerals  previously  confounded 
with  apophyllite,  which  Sir  John  Herschel  and  Sir  David 
Brewster  distinguished  by  those  names,  in  consequence  of  certain 
optical  properties  which  they  exhibit.  But  are  these  properties 
definite  distinctions  ?  and  are  there  any  external  differences  cor- 
responding to  them  ?  If  not,  can  we  consider  them  as  separate 
species  ?  and  if  not  separate  species,  ought  they  to  have  sepa- 
rate names  !  In  like  manner,  we  might  ask  if  Augite  and  Horn- 
blende are  really  the  same  species,  as  Gustavus  Rose  has  main- 
tained? if  Diallage  and  Hyperstkene  are  not  definitely  distin- 
guished, which  has  been  asserted  by  Kobell  ?  Till  such  questions 
are  settled,  we  cannot  have  a  fixed  nomenclature  in  mineralogy. 
What  appears  the  best  course  to  follow  in  the  present  state  of  the 
science,  I  shall  consider  when  we  come  to  speak  of  the  form  of 
technical  terms.  ^  -  , 


LXXVlii  APHORISMS   CONCERNING 

I  may,  however,  notice  here  that  the  main  forms  of  systema- 
tic nomenclature  are  two : — terms  which  are  produced  by  com- 
bining words  of  higher  and  lower  generality,  as  the  binary  names, 
consisting  of  the  name  of  the  genus  and  the  species,  generally 
employed  by  natural  historians  since  the  time  of  Linnaeus ; — and 
terms  in  which  some  relation  of  things  is  indicated  by  a  change 
in  the  form  of  the  word,  for  example,  an  alteration  of  its  termina- 
tion, of  which  kind  of  nomenclature  we  have  a  conspicuous 
example  in  the  modern  chemistry. 

APHORISM  X. 

New  terms  and  changes  ofterms^  which  are  not  needed  in  order  to 
express  truth,  are  to  be  avoided. 

As  the  Seventh  Aphorism  asserted  that  novelties  in  language 
may  be  and  ought  to  be  introduced,  when  they  aid  the  enunciation 
of  truths,  we  now  declare  that  they  are  not  admissible  in  any  other 
case.  New  terms  and  new  systems  of  terms  are  not  to  be  intro- 
duced, for  example,  in  virtue  of  their  own  neatness  or  symmetry, 
or  other  merits,  if  there  is  no  occasion  for  their  use. 

I  may  mention,  as  an  old  example  of  a  superfluous  attempt  of 
this  kind,  an  occurrence  in  the  history  of  astronomy.  In  1628 
John  Bayer  and  Julius  Schiller  devised  a  Ccelum  Christianum, 
in  which  the  common  names  of  the  planets,  &c.,  were  replaced  by 
those  of  Adam,  Moses,  and  the  Patriarchs.  The  twelve  Signs 
became  the  twelve  Apostles,  and  the  constellations  became  sacred 
places  and  things.  Peireskius,  who  had  to  pronounce  upon  the 
value  of  this  proposal,  praised  the  piety  of  the  inventors,  but  did 
not  approve,  he  said*,  the  design  of  perverting  and  confounding 
whatever  of  celestial  information  from  the  period  of  the  earliest 
memory  is  found  in  books. 

Nor  are  slight  anomalies  in  the  existing  language  of  science 
sufficient  ground  for  a  change,  if  they  do  not  seriously  interfere 
with  the  expression  of  our  knowledge.  Thus  Linnaeus  says-f- 
that  a  fair  generic  name  is  not  to  be  exchanged  for  another 
though  apter  one :  and  J  if  we  separate  an  old  genus  into  several, 

*  GASSENDI,  Vita  Pwreskii,  300.        t  Phil.  Bot.,  246.         §  /&.,  247. 


THE  LANGUAGE  OF  SCIENCE. 

we  must  try  to  find  names  for  them  among  the  synonyms  which 
describe  the  old  genus.  This  maxim  excludes  the  restoration 
of  ancient  names  long  disused,  no  less  than  the  needless  in" 
vention  of  new  ones.  Linnaeus  lays  down  this  rule  *  ;  and  adds, 
that  the  botanists  of  the  sixteenth  century  well  nigh  ruined  botany 
by  their  anxiety  to  recover  the  ancient  names  of  plants.  In  like 
manner  Cuvier~f-  laments  it  as  a  misfortune,  that  he  has  had  to 
introduce  many  new  names ;  and  declares  earnestly  that  he  has 
taken  great  pains  to  preserve  those  of  his  predecessors. 

The  great  bulk  which  the  synonymy  of  botany  and  of  mine- 
ralogy have  attained,  shows  us  that  this  maxim  has  not  been 
universally  attended  to.  In  these  cases,  however,  the  multiplica- 
tion of  different  names  for  the  same  kind  of  object  has  arisen  in 
general  from  ignorance  of  the  identity  of  it  under  different  circum- 
stances, or  from  the  want  of  a  system  which  might  assign  to  it  its 
proper  place.  But  there  are  other  instances,  in  which  the  multi- 
plication of  names  has  arisen  not  from  defect,  but  from  excess,  of 
the  spirit  of  system.  The  love  which  speculative  men  bear 
towards  symmetry  and  completeness  is  constantly  at  work,  to 
make  them  create  systems  of  classification  more  regular  and  more 
perfect  than  can  be  verified  by  the  facts :  and  as  good  systems 
are  closely  connected  with  a  good  nomenclature,  systems  thus 
erroneous  and  superfluous  lead  to  a  nomenclature  which  is  preju- 
dicial to  science.  For  although  such  a  nomenclature  is  finally 
expelled,  when  it  is  found  not  to  aid  us  in  expressing  the  true 
laws  of  nature,  it  may  obtain  some  temporary  sway,  during 
which,  and  even  afterwards,  it  may  be  a  source  of  much  confusion. 

We  have  a  conspicuous  example  of  such  a  result  in  the  geo- 
logical nomenclature  of  Werner  and  his  school.  Thus  it  was 
assumed,  in  Werner's  system,  that  his  First,  Second,  and  Third 
Flotz  Limestone,  his  Old  and  New  Red  Sandstone,  were  universal 
formations ;  and  geologists  looked  upon  it  as  their  business  to 
detect  these  strata  in  other  countries.  Names  were  thus  assigned 
to  the  rocks  of  various  parts  of  Europe,  which  created  immense 
perplexity  before  they  were  again  ejected.  The  geological  terms 
which  now  prevail,  for  instance,  those  of  Smith,  are  for  the  most 
*  Phil.  JBot.j  248.  t  Regne  Anim.j  Pref.  p.  xvi. 


LXXX  APHORISMS  CONCERNING 

part  not  systematic,  but  are  borrowed  from  accidents,  as  localities, 
or  popular  names ;  as  Oxford  Clay  and  Cornbrash ;  and  hence 
they  are  not  liable  to  be  thrust  out  on  a  change  of  system.  On  the 
other  hand  we  do  not  find  sufficient  reason  to  accept  the  system  of 
names  of  strata  proposed  by  Mr.  Conybeare  m  the  Introduction  to 
the  Geology  of  England  and  Wales,  according  to  which  the  Car- 
boniferous Rocks  are  the  Medial  Order, — having  above  them  the 
Supermedial  Order  (New  Red  Sand,  Oolites  and  Chalk),  and  above 
these  the  Superior  Order  (Tertiary  Rocks);  and  again, — having 
below,  the  Submedial  Order  (the  Transition  Rocks),  and  the 
Inferior  Order  (Mica Slate,  Gneiss,  Granite).  For  though  these 
names  have  long  been  proposed,  it  does  not  appear  that  they  are 
useful  in  enunciating  geological  truths.  We  may,  it  would  seem, 
pronounce  the  same  judgment  respecting  the  system  of  geological 
names  proposed  by  M.  Alexander  Brongniart,  in  his  Tableau, 
des  Terrains  qui  composent  Pecorce  du  Globe.  He  divides  these 
strata  into  nine  classes,  which  he  terms  Terrains  Alluviens, 
Lysiens,  Pyrogenes,  Clysmiens,  Yzemiens,  Hemilysiens,  Agaly- 
siens,  Plutoniques,  Vulcaniques.  These  classes  are  again  variously 
subdivided :  fhus  the  Terrains  Yzemiens  are  Thalassiques,  Pela- 
giques,  and  Abyssiques ;  and  the  Abyssiques  are  subdivided  into 
Lias,  Keuper,  Conchiliens,  Pceciliens,  Peneens,  Rudimentaires, 
Entritiques,  Houillers,  Carbonifers  and  Gres  Rouge  Ancien. 
Scarcely  any  amount  of  new  truths  would  induce  geologists  to 
burthen  themselves  at  once  with  this  enormous  system  of  new 
names  :  but  in  fact,  it  is  evident  that  any  portion  of  truth,  which 
any  author  can  have  brought  to  light,  may  be  conveyed  by  means 
of  a  much  simpler  apparatus.  Such  a  nomenclature  carries  its 
condemnation  on  its  own  face. 

Nearly  the  same  may  be  said  of  the  systematic  nomencla- 
ture proposed  for  mineralogy  by  Professor  Mohs.  Even  if  all 
his  Genera  be  really  natural  groups,  (a  doctrine  which  we  can 
have  no  confidence  in  till  they  are  confirmed  by  the  evidence  of 
chemistry,)  there  is  no  necessity  to  make  so  great  a  change  in 
the  received  names  of  minerals.  His  proceeding  in  this  respect, 
so  different  from  the  temperance  of  Linnaeus  and  Cuvier,  has 
probably  ensured  a  speedy  oblivion  to  this  part  of  his  system. 


THE  LANGUAGE  OF  SCIENCE.  LXXXL 

In  crystallography,  on  the  other  hand,  in  which  Mohs's  improve- 
ments have  been  very  valuable,  there  are  several  terms  introduced 
by  him,  as  rhombohedron,  scalenohedron,  hemihedral,  systems  of 
crystallization,  which  will  probably  be  a  permanent  portion  of 
the  language  of  science. 

I  may  remark,  in  general,  that  the  only  persons  who  succeed 
in  making  great  alterations  in  the  language  of  science,  are  not 
these  who  make  names  arbitrarily  and  as  an  exercise  of  ingenuity, 
but  those  who  have  much  new  knowledge  to  communicate ;  so 
that  the  vehicle  is  commended  to  general  reception  by  the  value 
of  what  it  contains.  It  is  only  eminent  discoverers  to  whom  the 
authority  is  conceded  of  introducing  a  new  system  of  names ; 
just  as  it  is  only  the  highest  authority  in  the  state  which  has  the 
power  of  putting  a  new  coinage  in  circulation. 

I  will  here  quote  some  judicious  remarks  of  Mr.  Howard,  which 
fall  partly  under  this  Aphorism,  and  partly  under  some  which 
follow.  He  had  proposed,  as  names  for  the  kinds  of  clouds,  the 
following :  Cirrus,  Cirrocumulus,  Cirrostratus,  Cumulostratus, 
Cumulus,  Nimbus,  Stratus.  In  an  abridgment  of  his  views,  given 
in  the  Supplement  to  the  Encyclopaedia  Britannica,  English  names 
were  proposed  as  the  equivalents  of  these ;  Curlcloud,  Sonder- 
cloud,  Wanecloud,  Twaincloud,  Stackencloud,  Eaincloud^  Fall- 
cloud.  Upon  these  Mr.  Howard  observes :  "  I  mention  these,  in 
order  to  have  the  opportunity  of  saying  that  I  do  not  adopt  them. 
The  names  for  the  clouds  which  I  deduced  from  the  Latin,  are 
but  seven  in  number,  and  very  easy  to  remember.  They  were 
intended  as  arbitrary  terms  for  the  structure  of  clouds,  and  the 
meaning  of  them  was  carefully  fixed  by  a  definition.  The  ob- 
server having  once  made  himself  master  of  this,  was  able  to  apply 
the  term  with  correctness,  after  a  little  experience,  to  the  subject 
under  all  its  varieties  of  form,  colour,  or  position.  The  new 
names,  if  meant  to  be  another  set  of  arbitrary  terms,  are  super- 
fluous ;  if  intended  to  convey  in  themselves  an  explanation  in 
English,  they  fail  in  this,  by  applying  to  some  part  or  circum- 
stance only  of  the  definition  ;  the  whole  of  which  must  be  kept  in 
view  to  study  the  subject  with  success.  To  take  for  an  example 
the  first  of  the  modifications.  The  term  cirrus  very  readily  takes 


LXXX11  APHORISMS   CONCERNING 

an  abstract  meaning,  equally  applicable  to  the  rectilinear  as  to 
the  flexuous  forms  of  the  subject.  But  the  name  of  curl-cloud 
will  not,  without  some  violence  to  its  obvious  sense,  acquire  this 
more  extensive  one:  and  will  therefore  be  apt  to  mislead  the 
reader  rather  than  further  his  progress.  Others  of  these  names 
are  as  devoid  of  a  meaning  obvious  to  the  English  reader,  as  the 
Latin  terms  themselves.  But  the  principal  objection  to  English 
or  any  other  local  terms,  remains  to  be  stated.  They  take  away 
from  the  nomenclature  its  general  advantage  of  constituting,  as 
far  as  it  goes,  an  universal  language,  by  means  of  which  the  intel- 
ligent of  every  country  may  convey  to  each  other  their  ideas 
without  the  necessity  of  translation."" 

I  here  adduce  these  as  examples  of  the  arguments  against 
changing  an  established  nomenclature.  As  grounds  of  selecting 
a  new  one,  they  may  be  taken  into  account  hereafter. 

APHORISM  XL 

Terms  which  imply  theoretical  views  are  admissible,  as  far  as  the 
theory  is  proved. 

IT  is  not  unfrequently  stated  that  the  circumstances  from 
which  the  names  employed  in  science  borrow  their  meaning, 
ought  to  be  facts  and  not  theories.  But  such  a  recommendation 
implies  a  belief  that  facts  are  rigorously  distinguished  from  theories 
and  directly  opposed  to  them ;  which  belief,  we  have  repeatedly 
seen,  is  unfounded.  When  theories  are  firmly  established,  they 
become  facts ;  and  names  founded  on  such  theoretical  views  are 
unexceptionable.  If  we  speak  of  the  minor  axis  of  Jupiter's 
orbit,  or  of  his  density,  or  of  the  angle  of  refraction,  or  the  length 
of  an  undulation  of  red  light,  we  assume  certain  theories ;  but 
nasmuch  as  the  theories  are  now  the  inevitable  interpretation  of 
ascertained  facts,  we  can  have  no  better  terms  to  designate  the 
conceptions  thus  referred  to.  And  hence  the  rule  which  we  must 
follow  is,  not  that  our  terms  must  involve  no  theory,  but  that 
they  imply  the  theory  only  in  that  sense  in  which  it  is  the  inter- 
pretation of  the  facts. 

For  example,  the  term  polarization  of  light  was  objected  to, 


THE   LANGUAGE   OF   SCIENCE.  LXXXlil 

as  involving  a  theory.  Perhaps  the  term  was  at  first  suggested 
by  conceiving  light  to  consist  of  particles  having  poles  turned  in 
a  particular  manner.  But  among  intelligent  speculators,  the 
notion  of  polarization  soon  reduced  itself  to  the  simple  conception 
of  opposite  properties  in  opposite  positions,  which  is  a  bare  state- 
ment of  the  fact :  and  the  term  being  understood  to  have  this 
meaning,  is  a  perfectly  good  term,  and  indeed  the  best  which  we 
can  imagine  for  designating  what  is  intended. 

I  need  hardly  add  the  caution,  that  names  involving  theo- 
retical views  not  in  accordance  with  facts  are  to  be  rejected. 
The  following  instances  exemplify  both  the  positive  and  the 
negative  application  of  this  maxim. 

The  distinction  of  primary  and  secondary  rocks  in  geology 
was  founded  upon  a  theory ;  namely,  that  those  which  do  not 
contain  any  organic  remains  were  first  deposited,  and  afterwards, 
those  which  contain  plants  and  animals.  But  this  theory  was 
insecure  from  the  first.  The  difficulty  of  making  the  separation 
which  it  implied,  led  to  the  introduction  of  a  class  of  transition 
rocks.  And  the  recent  researches  of  geologists  lead  them  to  the 
conclusion,  that  those  rocks  which  are  termed  primary,  may  be  the 
newest,  not  the  oldest,  productions  of  nature. 

In  order  to  avoid  this  incongruity,  other  terms  have  been  pro- 
posed as  substitutes  for  these.  Mr.  Lyell  remarks*,  that  granite, 
gneiss,  and  the  like,  form  a  class  which  should  be  designated  by 
a  common  name ;  which  name  should  not  be  of  chronological 
import.  He  proposes  hypogene^  signifying  "  nether-formed ;"  and 
thus  he  adopts  the  theory  that  they  have  not  assumed  their 
present  form  and  structure  at  the  surface,  but  determines  nothing 
of  the  period  when  they  were  produced. 

These  hypogene  rocks,  again,  he  divides  into  unstratified  or 
plutonic,  and  altered,  stratified,  or  metamorphic ;  the  latter  term 
implying  the  hypothesis  that  the  stratified  rocks  to  which  it  is 
applied  have  been  altered,  by  the  effect  of  fire  or  otherwise,  since 
they  were  deposited.  That  fossiliferous  strata,  in  some  cases  at 
least,  have  undergone  such  a  change,  is  demonstrable  from  facts  f. 

The  modern  nomenclature  of  chemistry  implies  the  oxygen 

*  Prim.  GeoL,  iv,  386.  t  JElem.  Geol.,  p.  17. 


LXXX1V  APHORISMS   CONCERNING 

theory  of  chemistry.  Hence  it  has  sometimes  been  objected  to. 
Thus  Davy,  in  speaking  of  the  Lavoisierian  nomenclature,  makes 
the  following  remarks,  which,  however  plausible  they  may  sound, 
will  be  found  to  be  utterly  erroneous*.  "  Simplicity  and  pre- 
cision ought  to  be  the  characteristics  of  a  scientific  nomenclature  : 
words  should  signify  things,  or  the  analogies  of  things,  and  not 
opinions.  ...  A  substance  in  one  age  supposed  to  be  simple,  in 
another  is  proved  to  be  compound,  and  vice  versa.  A  theoretical 
nomenclature  is  liable  to  continual  alterations  :  oxygenated  muri- 
atic acid  is  as  improper  a  term  as  dephlogisticated  marine  acid. 
Every  school  believes  itself  to  be  in  the  right :  and  if  every  school 
assumes  to  itself  the  liberty  of  altering  the  names  of  chemical 
substances  in  consequence  of  new  ideas  of  their  composition,  there 
can  be  no  permanency  in  the  language  of  the  science ;  it  must 
always  be  confused  and  uncertain.  Bodies  which  are  similar  to 
each  other  should  always  be  classed  together ;  and  there  is  a 
presumption  that  their  composition  is  analogous.  Metals,  earths, 
alkalis,  are  appropriate  names  for  the  bodies  they  represent,  and 
independent  of  all  speculation :  whereas  oxides,  sulphurets,  and 
muriates  are  terms  founded  upon  opinions  of  the  composition  of 
bodies,  some  of  which  have  been  already  found  erroneous.  The 
least  dangerous  mode  of  giving  a  systematic  form  to  a  language 
seems  to  be  to  signify  the  analogies  of  substances  by  some  com- 
mon sign  affixed  to  the  beginning  or  the  termination  of  the  word. 
Thus  as  the  metals  have  been  distinguished  by  a  termination  in 
um,  as  aurum,  so  their  calciform  or  oxidated  state  might  have 
been  denoted  by  a  termination  in  a,  as  aura :  and  no  progress, 
however  great,  in  the  science  could  render  it  necessary  that 
such  a  mode  of  appellation  should  be  changed." 

These  remarks  are  founded  upon  distinctions  which  have  no 
real  existence.  We  cannot  separate  things  from  their  properties, 
nor  can  we  consider  their  properties  and  analogies  in  any  other 
way  than  by  having  opinions  about  them.  By  contrasting  analo- 
gies with  opinions,  it  might  appear  as  if  the  author  maintained 
that  there  were  certain  analogies  about  which  there  was  no  room 
for  eironeous  opinions.  Yet  the  analogies  of  chemical  compounds, 
*  Elements  of  Chem.  Phil.,  p.  46. 


THE  LANGUAGE  OF  SCIENCE.  LXXXV 

arc,  in  fact,  those  points  which  have  heen  most  the  subject  of  differ- 
ence of  opinion,  and  on  which  the  revolutions  of  theories  have 
have  most  changed  men's  views.  As  an  example  of  analogies 
which  are  still  recognized  under  alterations  of  theory,  the  writer 
gives  the  relation  of  a  metal  to  its  oxide  or  calciform  state.  But 
this  analogy  of  metallic  oxides,  as  Red  Copper  or  Iron  Ore,  to  Calx, 
or  burnt  lime,  is  very  far  from  being  self-evident ; — so  far  indeed, 
that  the  recognition  of  the  analogy  was  a  great  step  in  chemical 
theory.  The  terms  which  he  quotes,  oxygenated  muriatic  acid 
(and  the  same  may  be  said  of  dephlogisticated  marine  acid?)  if 
improper,  are  so  not  because  they  involve  theory,  but  because  they 
involve  false  theory ; — not  because  those  who  framed  them  did 
not  endeavour  to  express  analogies,  but  because  they  expressed 
analogies  about  which  they  were  mistaken.  Unconnected  names, 
as  metals,  earths,  alkalis,  are  good  as  the  basis  of  a  systematic 
nomenclature,  but  they  are  not  substitutes  for  such  a  nomencla- 
ture. A  systematic  nomenclature  is  an  instrument  of  great  utility 
and  power,  as  the  modern  history  of  chemistry  has  shown.  It 
would  be  highly  unphilosophical  to  reject  the  use  of  such  an  in- 
strument, because,  in  the  course  of  the  revolutions  of  science,  we 
may  have  to  modify,  or  even  to  remodel  it  altogether.  Its  utility 
is  not  by  that  means  destroyed.  It  has  retained,  transmitted,  and 
enabled  us  to  reason  upon,  the  doctrines  of  the  earlier  theory,  so 
far  as  they  are  true ;  and  when  this  theory  is  absorbed  into  a 
more  comprehensive  one,  (for  this,  and  not  its  refutation,  is  the 
end  of  a  theory  so  far  as  it  is  true,)  the  nomenclature  is  easily  tran- 
slated into  that  which  the  new  theory  introduces.  "We  have  seen, 
in  the  history  of  astronomy,  how  valuable  the  theory  of  epicycles 
was,  in  its  time :  the  nomenclature  of  the  relations  of  a  planet's 
orbit,  which  that  theory  introduced,  was  one  of  Kepler's  resources 
in  discovering  the  elliptical  theory ;  and,  though  now  superseded, 
is  still  readily  intelligible  to  astronomers. 

This  is  not  the  place  to  discuss  the  reasons  for  the  form  of 
scientific  terms ;  otherwise  we  might  ask,  in  reference  to  the 
objections  to  the  Lavoisierian  nomenclature,  if  such  forms  as 
aurum  and  aura  are  good  to  represent  the  absence  or  presence  of 
oxygen,  why  such  forms  as  sulphite  and  sulphate  are  not  equally 


LXXXV1  APHORISMS   CONCERNING 

good  to  represent  the  presence  of  what  we  may  call  a  smaller  or 
larger  dose  of  oxygen,  so  long  as  the  oxygen  theory  is  admitted  in 
its  present  form  ;  and  to  indicate  still  the  difference  of  the  same 
substances,  if  under  any  change  of  theory  it  should  come  to  be 
interpreted  in  a  new  manner. 

But  I  do  not  now  dwell  upon  such  arguments,  my  object  in 
this  place  being  to  show  that  terms  involving  theory  are  not  only 
allowable,  if  understood  so  far  as  the  theory  is  proved,  but  of 
great  value,  and  indeed  of  indispensable  use,  in  science.  The  ob- 
jection to  them  is  inconsistent  with  the  objects  of  science.  If, 
after  all  that  has  been  done  in  chemistry  or  any  other  science,  we 
have  arrived  at  no  solid  knowledge,  no  permanent  truth; — if  all 
that  we  believe  now  may  be  proved  to  be  false  tomorrow  ; — then 
indeed  our  opinions  and  theories  are  corruptible  elements,  on  which 
it  would  be  unwise  to  rest  any  thing  important,  and  which  we 
might  wish  to  exclude,  even  from  our  names.  But  if  our  knowledge 
has  no  more  security  than  this,  we  can  find  no  reason  why  we 
should  wish  to  have  names  of  things,  since  the  names  are  needed 
mainly  that  we  may  reason  upon  and  increase  our  knowledge  such 
as  it  is.  If  we  are  condemned  to  endless  alternations  of  varying 
opinions,  then,  no  doubt,  our  theoretical  terms  may  be  a  source  of 
confusion  ;  but  then,  where  would  be  the  advantage  of  their  being 
otherwise?  what  would  be  the  value  of  words  which  should 
express  in  a  more  precise  manner  opinions  equally  fleeting  ?  It 
will  perhaps  be  said,  our  terms  must  express  facts,  not  theories : 
but  of  this  distinction  so  applied  we  have  repeatedly  shown  the 
futility.  Theories  firmly  established  are  facts.  Is  it  not  a  fact 
that  the  rusting  of  iron  arises  from  the  metal  combining  with  the 
oxygen  of  the  atmosphere  ?  Is  it  not  a  fact  that  a  combination  of 
oxygen  and  hydrogen  produces  water  ?  That  our  terms  should 
express  such  facts,  is  precisely  what  we  are  here  inculcating. 

Our  examination  of  the  history  of  science  has  led  us  to  a  view 
very  different  from  that  which  represents  it  as  consisting  in  the 
succession  of  hostile  opinions.  It  is,  on  the  contrary,  a  progress,  in 
which  each  step  is  recognized  and  employed  in  the  succeeding  one. 
Every  theory,  so  far  as  it  is  true,  (and  all  that  have  prevailed  ex- 
tensively and  long,  contain  a  large  portion  of  truth,)  is  taken  up 


THE  LANGUAGE  OF  SCIENCE.  LXXXV11 

into  the  theory  which  succeeds  and  seems  to  expel  it.  All  the 
narrower  inductions  of  the  first  are  included  in  the  more  compre- 
hensive generalizations  of  the  second.  And  this  is  performed 
mainly  by  means  of  such  terms  as  we  are  now  considering ; — 
terms  involving  the  previous  theory.  It  is  by  means  of  such 
terms,  that  the  truths  at  first  ascertained  become  so  familiar  and 
manageable,  that  they  can  be  employed  as  elementary  facts  in  the 
formation  of  higher  inductions. 

These  principles  must  be  applied  also,  though  with  great  cau- 
tion, and  in  a  temperate  manner,  even  to  descriptive  language. 
Thus  the  mode  of  describing  the  forms  of  crystals  adopted  by 
Werner  and  Rome  de  Tlsle  was  to  consider  an  original  form,  from 
which  other  forms  are  derived  by  truncatiom  of  the  edges  and  the 
angles.  Haiiy^s  method  of  describing  the  same  forms,  was  to 
consider  them  as  built  up  of  rows  of  small  solids,  the  angles  being 
determined  by  the  decrements  of  these  rows.  Both  these  methods 
of  description  involve  hypothetical  views ;  and  the  last  was 
intended  to  rest  on  a  true  physical  theory  of  the  constitution  of 
crystals.  Both  hypotheses  are  doubtful  or  false  :  yet  both  these 
methods  are  good  as  modes  of  description :  nor  is  Hatty's  termi- 
nology vitiated,  if  we  suppose  (as  in  fact  we  must  suppose  in 
many  instances,)  that  crystalline  bodies  are  not  really  made  up  of 
such  small  solids.  The  mode  of  describing  an  octahedron  of  fluor 
spar,  as  derived  from  the  cube,  by  decrements  of  one  row  on  all  the 
edges,  would  still  be  proper  and  useful  as  a  description,  whatever 
judgment  we  should  form  of  the  material  structure  of  the  body. 
But  then,  we  must  consider  the  solids  which  are  thus  introduced 
into  the  description  as  merely  hypothetical  geometrical  forms, 
serving  to  determine  the  angles  of  the  faces.  It  is  in  this  way 
alone  that  Haiiy's  nomenclature  can  now  be  retained. 

In  like  manner  we  may  admit  theoretical  views  into  the 
descriptive  phraseology  of  other  parts  of  Natural  History :  and 
the  theoretical  terms  will  replace  the  obvious  images,  in  propor- 
tion as  the  theory  is  generally  accepted  and  familiarly  applied. 
For  example,  in  speaking  of  the  Honeysuckle,  we  may  say  that 
the  upper  leaves  are  perfoliate>  meaning  that  a  single  orbicular 
leaf  is  perforated  by  the  stalk  or  threaded  upon  it.  Here  is  an 


LXXXV111  APHORISMS   CONCERNING 

image  which  sufficiently  conveys  the  notion  of  the  form.  But  it  is 
now  generally  recognized  that  this  apparent  single  leaf  is,  in  fact, 
two  opposite  leaves  joined  together  at  their  bases.  If  this  were 
doubted,  it  may  be  proved  by  comparing  the  upper  leaves  with  the 
lower,  which  are  really  separate  and  opposite.  Hence  the  term 
connate  is  applied  to  these  conjoined  opposite  leaves,  implying  that 
they  grow  together ;  or  they  are  called  connato-perfoliate.  Again  ; 
formerly  the  corolla  was  called  monopetalous  or  polypetalous,  as  it 
consisted  of  one  part  or  of  several :  but  it  is  now  agreed  among 
botanists  that  those  corollas  which  appear  to  consist  of  a  single 
part,  are,  in  fact,  composed  of  several  soldered  together ;  hence 
the  term  gamopetalous  is  now  employed  (by  Decandolle  and  his 
followers)  instead  of  monopetalous*. 

In  this  way  the  language  of  natural  history  not  only  expresses, 
but  inevitably  implies,  general  laws  of  nature ;  and  words  are 
thus  fitted  to  aid  the  progress  of  knowledge  in  this,  as  in  other 
provinces  of  science. 

APHORISM  XII. 

If  terms  are  systematically  good,  they  are  not  to  be  rejected  because 
they  are  etymologically  inaccurate. 

TERMS  belonging  to  a  system  are  defined,  not  by  the  meaning 
of  their  radical  words,  but  by  their  place  in  the  system.  That 
they  should  be  appropriate  in  their  signification,  aids  the  processes 
of  introducing  and  remembering  them,  and  should  therefore  be 
carefully  attended  to  by  those  who  invent  and  establish  them  ; 
but  this  once  done,  no  objections  founded  upon  their  etymo- 
logical import  are  of  any  material  weight.  We  find  no  inconve- 
nience in  the  circumstance  that  geometry  means  the  measuring  of 
the  earth,  that  the  name  porphyry  is  applied  to  many  rocks  which 
have  no  fiery  spots,  as  the  word  implies,  and  oolite  to  strata  which 
have  no  roelike  -structure.  In  like  manner,  if  the  term  pwcilite 

*  On  this  subject,  see  ILLIGER,  Versuch  einer  Systematischen  Vollstandigen 
Terminologie  fur  das  Thierreich  und  Pflanzenreich,  (1810.)  DECANDOLLE, 
Theorie  Elementaire  de  la  Botanique. 


THE  LANGUAGE  OF  SCIENCE.  LXXxix 

were  already  generally  received,  as  the  name  of  a  certain  group  of 
strata,  it  would  be  no  valid  ground  for  quarreling  with  it,  that  this 
group  was  not  always  variegated  in  colour,  or  that  other  groups 
were  equally  variegated:  although  undoubtedly  in  introducing  such 
a  term,  care  should  be  taken  to  make  it  as  distinctive  as  possible. 
It  often  happens,  as  we  have  seen,  that  by  the  natural  progress  of 
changes  in  language,  a  word  is  steadily  confirmed  in  a  sense  quite 
different  from  its  etymological  import.  But  though  we  may 
accept  such  instances,  we  must  not  wantonly  attempt  to  imitate 
them.  I  say,  not  wantonly  :  for  if  the  progress  of  scientific  iden- 
tification compel  us  to  follow  any  class  of  objects  into  circum- 
stances where  the  derivation  of  the  term  is  inapplicable,  we  may 
still  consider  the  term  as  an  unmeaning  sound,  or  rather  an  his- 
torical symbol,  expressing  a  certain  member  of  our  system.  Thus 
if,  in  following  the  course  of  the  mountain  or  carboniferous  lime- 
stone, we  find  that  in  Ireland  it  does  not  form  mountains  nor 
contain  coal,  we  should  act  unwisely  in  breaking  down  the 
nomenclature  in  which  our  systematic  relations  are  already  ex- 
pressed, in  order  to  gain,  in  a  particular  case,  a  propriety  of  lan- 
guage which  has  no  scientific  value. 

All  attempts  to  act  upon  the  maxim  opposite  to  this,  and  to 
make  our  scientific  names  properly  descriptive  of  the  objects,  have 
failed  and  must  fail.  For  the  marks  which  really  distinguish  the 
natural  classes  of  objects,  are  by  no  means  obvious.  The  discovery 
of  them  is  one  of  the  most  important  steps  in  science;  and  when 
they  are  discovered,  they  are  constantly  liable  to  exceptions, 
because  they  do  not  contain  the  essential  differences  of  the  classes. 
The  natural  order  Umbellatw^  in  order  to  be  a  natural  order,  must 
contain  some  plants  which  have  not  umbels,  as  Eryngium*.  "  In 
such  cases,"  said  Linnaeus,  "  it  is  of  small  import  what  you  call 
the  order,  if  you  take  a  proper  series  of  plants,  and  give  it  some 
name  which  is  clearly  understood  to  apply  to  the  plants  you  have 
associated."  "  I  have,"  he  adds,  "  followed  the  rule  of  borrowing 
the  name  a  fortiori,  from  the  principal  feature." 

The  distinction  of  crystals  into  systems  according  to  the  degree 
of  symmetry  which  obtains  in  them,  has  been  explained  elsewhere. 
«  See  Hist.  Tnd,  Sd.9  iii.  324. 

VOL.  i.  g 


XC  APHORISMS  CONCERNING 

Two  of  these  systems,  of  which  the  relation  as  to  symmetry  might 
be  expressed  by  saying  that  one  is  square  pyramidal  and  the  other 
oblong  pyramidal,  or  the  first  square  prismatic  and  the  second 
oblong  prismatic,  are  termedby  Mohs,  the  first,  Pyramidal,  and  the 
second  Prismatic.  And  it  may  be  doubted  whether  it  is  worth 
while  to  invent  other  terms,  though  these  are  thus  defective  in 
characteristic  significance.  As  an  example  of  a  needless  rejection 
of  old  terms  in  virtue  of  a  supposed  impropriety  in  their  mean- 
ing, I  may  mention  the  attempt  made  in  the  last  edition  of  Haiiy's 
Mineralogy,  to  substitute  autopside  and  heteropside  for  metallic  and 
unmetattic.  It  was  supposed  to  be  proved  that  all  bodies  have 
a  metal  for  their  basis  ;  and  hence  it  was  wished  to  avoid  the  term 
unmetattic.  But  the  words  metallic  and  unmetattic  may  mean 
that  minerals  seem  metallic  and  unmetallic,  just  as  well  as  if  they 
contained  the  element  opside  to  imply  this  seeming.  The  old 
names  express  all  that  the  new  express,  and  with  more  simpli- 
city, and  therefore  should  not  be  disturbed. 

The  maxim  on  which  we  are  now  insisting,  that  we  are  not  to 
be  too  scrupulous  about  the  etymology  of  scientific  terms,  may,  at 
first  sight,  appear  to  be  at  variance  with  our  Fourth  Aphorism,  that 
words  used  technically  are  to  retain  their  common  meaning  as  far  as 
possible.  But  it  must  be  recollected,  that  in  the  Fourth  Aphorism 
we  spoke  of  common  words  appropriated  as  technical  terms ;  we 
here  speak  of  words  constructed  for  scientific  purposes.  And 
although  it  is,  perhaps,  impossible  to  draw  a  broad  line  between 
these  two  classes  of  terms,  still  the  rule  of  propriety  may  be 
stated  thus  :  In  technical  terms,  deviations  from  the  usual  mean- 
ing of  words  are  bad  in  proportion  as  the  words  are  more  familiar 
in  our  own  language.  Thus  we  may  apply  the  term  Cirrus 
to  a  cloud  composed  of  filaments,  even  if  these  filaments  are 
straight ;  but  to  call  such  a  cloud  a  Curl  cloud  would  be  much 
more  harsh. 

Since  the  names  of  things,  and  of  classes  of  things,  when  con- 
structed so  as  to  involve  a  description,  are  constantly  liable  to  be- 
come bad,  the  natural  classes  shifting  away  from  the  descriptive 
marks  thus  prematurely  and  casually  adopted,  I  venture  to  lay 
down  the  following  maxim. 


THE  LANGUAGE  OF  SCIENCE. 


APHORISM  XIII. 

The  fundamental  terms  of  a  system  of  Nomenclature  may  "be  conve- 
niently borrowed  from  casual  or  arbitrary  circumstances. 

FOR  instance,  the  names  of  plants,  of  minerals,  and  of  geolo- 
gical strata,  may  be  taken  from  the  places  where  they  occur  con- 
spicuously or  in  a  distinct  form  ;  as  Parietaria^  Parnassia,  Chal- 
cedony, Arragonite,  Silurian  system,  Purbeck  limestone.  These 
names  may  be  considered  as  at  first  supplying  standards  of  refer- 
ence ;  for  in  order  to  ascertain  whether  any  rock  be  Purbeck  lime- 
stone, we  might  compare  it  with  the  rocks  in  the  Isle  of  Purbeck. 
But  this  reference  to  a  local  standard  is  of  authority  only  till  the 
place  of  the  object  in  the  system,  and  its  distinctive  marks,  are 
ascertained.  It  would  not  vitiate  the  above  names,  if  it  were 
found  that  the  Parnassia  does  not  grow  on  Parnassus;  that 
Chalcedony  is  not  found  in  Chalcedon  ;  or  even  that  Arragon- 
ite  no  longer  occurs  in  Arragon  ;  for  it  is  now  firmly  established 
as  a  mineral  species.  Even  in  geology  such  a  reference  is  arbi- 
trary, and  may  be  superseded,  or  at  least  modified,  by  a  more  sys- 
tematic determination.  Alpine  limestone  is  no  longer  accepted 
as  a  satisfactory  designation  of  a  rock,  now  that  we  know  the 
limestone  of  the  Alps  to  be  of  various  ages. 

Again,  names  of  persons,  either  casually  connected  with  the 
object,  or  arbitrarily  applied  to  it,  may  be  employed  as  designa- 
tions. This  has  been  done  most  copiously  in  botany,  as  for  ex- 
am])\e,Nicotiana,  Dalilia^FucJma^Jungermannia^  Lonicera.  And 
Linnaeus  has  laid  down  rules  for  restricting  this  mode  of  per- 
petuating the  memory  of  men,  in  the  names  of  plants.  Those 
generic  names,  he  says*,  which  have  been  constructed  to  preserve 
the  memory  of  persons  who  have  deserved  well  of  botany,  are  to 
be  religiously  retained.  This,  he  adds,  is  the  sole  and  supreme 
reward  of  the  botanist's  labours,  and  must  be  carefully  guarded 
and  scrupulously  bestowed,  as  an  encouragement  and  an 
honour.  Still  more  arbitrary  are  the  terms  borrowed  from 
the  names  of  the  gods  and  goddesses,  heroes  and  heroines  of 
*  Phil  Bot.,  241. 

9* 


XC11  APHORISMS  CONCERNING 

antiquity,  to  designate  new  genera  in  those  departments  of 
natural  history  in  which  so  many  have  been  discovered  in 
recent  times  as  to  weary  out  all  attempts  at  descriptive  nomen- 
clature. Cuvier  has  countenanced  this  method.  "  I  have  had  to 
frame  many  new  names  of  genera  and  sub-genera,"  he  says  *, 
"  for  the  sub-genera  which  I  have  established  weru  so  numerous 
and  various,  that  the  memory  is  not  satisfied  with  numerical  in- 
dications. These  I  have  chosen  either  so  as  to  indicate  some  cha- 
racter, or  among  the  usual  denominations,  which  I  have  latinized, 
or  finally,  after  the  example  of  Linnaeus,  among  the  names  of 
mythology,  which  are  in  general  agreeable  to  the  ear,  and  which 
are  far  from  being  exhausted." 

This  mode  of  framing  names  from  the  names  of  persons  to 
whom  it  was  intended  to  do  honour,  has  been  employed  also  in 
the  mathematical  and  chemical  sciences ;  but  such  names  have 
rarely  obtained  any  permanence,  except  when  they  recorded  an 
inventor  or  discoverer.  Some  of  the  constellations,  indeed,  have 
retained  such  appellations,  as  Berenice's  Hair ;  and  the  new  star 
which  shone  out  in  the  time  of  Csesar,  would  probably  have  re- 
tained the  name  given  to  it,  of  the  Julian  Star,  if  it  had  not 
disappeared  again  soon  after.  In  the  map  of  the  Moon,  almost 
all  the  parts  have  had  such  names  imposed  upon  them  by  those  who 
have  constructed  such  maps,  and  these  names  have  very  properly 
been  retained.  But  the  names  of  new  planets  and  satellites  thus 
suggested  have  not  been  generally  accepted ;  as  the  Medicean 
stars,  the  name  employed  by  Galileo  for  the  satellites  of  Jupiter, 
the  Georgium  Sidus,  the  appellation  proposed  by  Herschel  for 
Uranus  when  first  discovered  ;  Ceres  Ferdinandea,  the  name 
which  Piazzi  wished  to  impose  on  the  small  planet  Ceres.  The 
names  given  to  astronomical  tables  by  the  astronomers  who  con- 
structed them  have  been  most  steadily  adhered  to,  being  indeed 
names  of  books,  and  not  of  natural  objects.  Thus  there  were 
the  Ilchanic,  the  Alphonsine,  the  Rudolphine,  the  Carolinian 
Tables.  Comets  which  have  been  ascertained  to  be  periodical, 
have  very  properly  had  assigned  to  them  the  name  of  the  person 
.  who  established  this  point ;  and  of  these  we  have  thus,  Halle^s, 
*  Regne  An.,  p.  xvi. 


THE  LANGUAGE  OF  SCIENCE.  Xclii 

Enckes,  and  Gambarfs  Comets;  the  latter  is  often  unjustly 
called  Bielas  comet. 

In  the  case  of  discoveries  in  science  or  inventions  of  appa- 
ratus, the  name  of  the  inventor  is  very  properly  employed  as  the 
designation.  Thus  we  have  the  Torricellian  \racuum,  the  Voltaic 
Pile,  Fahrenheit's  Thermometer.  And  in  the  same  manner  with 
regard  to  laws  of  nature,  we  have  Kepler's  Laws,  Boyle  or  Mari- 
ottes  law  of  the  elasticity  of  air,  Huyghens's  law  of  double  refrac- 
tion, Newton's  scale  of  colours.  Descartes'  law  of  refraction  is  an 
unjust  appellation;  for  the  discovery  of  the  law  of  sines  was  made 
by  Snell.  In  deductive  mathematics,  where  the  invention  of  a 
theorem  is  generally  a  more  definite  step  than  an  induction,  this 
mode  of  designation  is  more  common,  as  Demoivre**  Theorem, 
Maclaurin's  Theorem,  Lagrange^s  Theorem,  Eulerian  Integrals. 

In  the  History  of  Science*,  I  have  remarked  that  in  the  dis- 
covery of  what  is  termed  galvanism,  Volta's  office  was  of  a  higher 
and  more  philosophical  kind  than  that  of  Galvani ;  and  I  have, 
on  this  account,  urged  the  propriety  of  employing  the  term  vol- 
taic, rather  than  galvanic  electricity.  I  may  add  that  the  elec- 
tricity of  the  common  machine  is  often  placed  in  contrast  with 
this,  and  appears  to  require  an  express  name.  Mr.  Faraday  calls 
it  common,  or  machine  electricity ;  but  I  think  that  franklinic 
electricity  would  form  a  more  natural  correspondence  with  vol- 
taic, and  would  be  well  justified  by  Franklin's  place  in  the  his- 
tory of  that  part  of  the  subject. 

APHORISM  XIV. 

In  forming  a  Terminology,  words  may  be  invented  when  necessary, 
but  they  cannot  be  conveniently  borrowed  from  casual  or  arbi- 
trary circumstances. 

IT  will  be  recollected  that  Terminology  is  a  language  em- 
ployed for  describing  objects.  Nomenclature,  a  body  of  names  of 
the  objects  themselves.  The  names,  as  was  stated  in  the  last 
maxim,  may  be  arbitrary;  but  the  descriptive  terms  must  be 


XC1V  APHORISMS  CONCERNING 

borrowed  from  words  of  suitable  meaning  in  the  modern  or  the 
classical  languages.  Thus  the  whole  terminology  which  Linnaeus 
introduced  into  botany,  is  founded  upon  the  received  use  of  Latin 
words,  although  he  defined  their  meaning  so  as  to  make  it  precise 
when  it  was  not  so,  according  to  Aphorism  V.  But  many  of  the 
terms  were  invented  by  him  and  other  botanists,  as  Perianth, 
Nectary,  Pericarp ;  so  many,  indeed,  as  to  form,  along  with  the 
others,  a  considerable  language.  Many  of  the  terms  which  are 
now  become  familiar  were  originally  invented  by  writers  on 
botany.  Thus  the  word  petal,  for  one  division  of  the  corolla,  was 
introduced  by  Fabius  Columna.  The  term  sepal  was  devised  by 
Neckar  to  express  each  of  the  divisions  of  the  calyx.  And  up 
to  the  most  recent  times,  new  denominations  of  parts  and  con- 
ditions of  parts  have  been  devised  by  botanists,  when  they  found 
them  necessary,  in  order  to  mark  important  differences  or  resem- 
blances. Thus  the  general  receptacle  of  the  flower,  as  it  is 
termed  by  Linnaeus,  or  torus,  by  Salisbury,  is  continued  into  organs 
\vhich  carry  the  stamina  and  pistil,  or  the  pistil  alone,  or  the 
whole  flower ;  this  organ  has  hence  been  termed*  gonophore, 
carpophore,  and  anthophore,  in  these  cases. 

In  like  manner  when  Cuvier  had  ascertained  that  the  lower 
jaws  of  Saurians  consisted  always  of  six  pieces  having  definite  re- 
lations of  form  and  position,  he  gave  names  to  them,  and  termed 
them  respectively  the  dental,  the  angular,  the  coronoid,  the  articu- 
lar, the  complementary,  and  the  opercular  bones. 

In  all  these  cases,  the  descriptive  terms  thus  introduced  have 
been  significant  in  their  derivation.  An  attempt  to  circulate  a 
perfectly  arbitrary  word  as  a  means  of  description  would  probably 
be  unsuccessful.  We  have,  indeed,  some  examples  approaching 
to  arbitrary  designations,  in  the  Wernerian  names  of  colours, 
which  are  a  part  of  the  terminology  of  Natural  History.  Many 
of  these  names  are  borrowed  from  natural  resemblances,  as  Auri- 
cula purple,  Apple  green,  Straw  yellow  ;  but  the  names  of  others 
are  taken  from  casual  occurrences,  mostly,  however,  such  as  were 
already  recognized  in  common  language,  as  Prussian  blue,  Dutch 
orange,  King's  yellow. 

*  DECANDOLLE'S  Th.  EL,  405. 


THE    LANGUAGE    OF    SCIENCE.  XCV 

The  extension  of  arbitrary  names  in  scientific  terminology  is 
by  no  means  to  be  encouraged.     I  may  mention  a  case  in  which 
it  was  very  properly  avoided.       When  Mr.  Faraday's  researches 
on  Voltaic  electricity  had  led   him  to  perceive  the  great  impro- 
priety of  the   term  poles,  as  applied  to  the  apparatus,  since  the 
processes  have  not  reference  to  any  opposed  points,  but  to  two 
opposite  directions  of  a  path,  he  very  suitably  wished  to  substi- 
tute for  the  phrases  positive  pole  and  negative  pole  two  words  end- 
ing in  ode,  from   oSos,  a  way.     A   person   who  did  not  see  the 
value  of  our  present  maxim,  that  descriptive  terms  should  be  de- 
scriptive in  their   origin,  might  have  proposed  words   perfectly 
arbitrary,  as  Alphode  and  Betode :  or,  if  he  wished  to  pay  a  tribute 
of  respect  to  the  discoverers  in  this  department  of  science,  Gal- 
vanode  and  VoUaode.     But  such  words  would  very  justly  have 
been  rejected  by  Mr.  Faraday,  and  would  hardly  have  obtained 
any  general  currency  among  men  of  science.     Zincode  and  Pla- 
tinode,  terms  derived  from  the  metal  which,  in  one  modification 
of  the  apparatus,  forms  what  was  previously  termed  the  pole,  are 
to  be  avoided,   because   in   their  origin   too   much    is    casual; 
and  they  are  not  a  good  basis  for  derivative  terms.     The  pole 
at  which  the  zinc  is,  is  the  Anode  or  Cathode,  according  as  it 
is  associated  with  different  metals.     Either  the  zincode  must  some- 
times mean  the  pole  at  which  the  Zinc  is,  and  at  other  times  that 
at  which  the  Zinc  is  not,  or  else  we  must  have  as  many  names 
for  poles  as  there  are  metals.     Anode  and  Cathode,  the   terms 
which  Mr.  Faraday  adopted,  were  free  from  these  objections;  for 
they  refer  to  a  natural  standard  of  the  direction  of  the  voltaic 
current,  in  a  manner  which,  though  perhaps  not  obvious  at  first 
sight,  is  easily  understood  and  retained.      Anode  and  Cathode, 
the  rising  and  the  setting  way,  are  the  directions  which  corre- 
spond to  east  and  west  in  that  voltaic  current  to  which  we  must 
ascribe  terrestrial  magnetism.     And  with  these  words  it  was  easy 
to  connect  ariion  and  catJiion,  to  designate  the  opposite  elements 
which  are  separated  and  liberated  at  the  two  electrodes. 

The  following  Aphorisms   respect   the  Form   of  Technical 
Terms. 

By  the  Form  of  Terms,  I  mean  their  philological  conditions ; 


XCV1  APHORISMS    CONCERNING 

as,  for  example,  from  what  languages  they  may  be  borrowed,  by 
what  modes  of  inflexion  they  must  be  compounded,  how  their 
derivatives  are  to  be  formed,  and  the  like.  In  this,  as  in  other 
parts  of  the  subject,  I  shall  not  lay  down  a  system  of  rules,  but 
shall  propose  a  few  maxims. 

APHORISM  XV. 

The  two  main  conditions  of  the  Form  of  technical  terms  are,  that 
they  must  be  generally  intelligible,  and  susceptible  of  such  gram- 
matical relations  as  their  scientific  use  requires. 

THESE  conditions  may  at  first  appear  somewhat  vague,  but  it 
will  be  found  that  they  are  as  definite  as  we  could  make  them, 
without  injuriously  restricting  ourselves.  It  will  appear,  more- 
over, that  they  have  an  important  bearing  upon  most  of  the  ques- 
tions respecting  the  form  of  the  words  which  come  before  us ; 
and  that  if  we  can  succeed  in  any  case  in  reconciling  the  two 
conditions,  we  obtain  terms  which  are  practically  good,  whatever 
objections  may  be  urged  against  them  from  other  considerations. 

1.  The  former  condition,  for  instance,  bears  upon  the 
question  whether  scientific  terms  are  to  be  taken  from  the 
learned  languages,  Greek  and  Latin,  or  from  our  own. 
And  the  latter  condition  very  materially  affects  the  same  ques- 
tion, since  in  English  we  have  scarcely  any  power  of  inflect- 
ing our  words;  and  therefore  must  have  recourse  to  Greek  or 
Latin  in  order  to  obtain  terms  which  admit  of  grammatical  modi- 
fication. If  we  were  content  with  the  term  Heat  to  express  the 
science  of  heat,  still  it  would  be  a  bad  technical  term,  for  we 
cannot  derive  from  it  an  adjective  like  thermotical.  If  bed  or 
layer  were  an  equally  good  term  with  stratum,  we  must  still  retain 
the  latter,  in  order  that  we  may  use  the  derivative  stratification, 
for  which  the  English  words  cannot  produce  an  equivalent  sub- 
stitute. We  may  retain  the  words  lime  andyfoVztf,  but  their  adjec- 
tives for  scientific  purposes  are  not  limy  and  flinty,  but  calcareous 
and  siliceous;  and  hence  we  are  able  to  form  a  compound,  as 
calcareo- siliceous,  which  we  could  not  do  with  indigenous 


THE   LANGUAGE   OF    SCIENCE.  XCVii 

words.  We  might  fix  the  phrases  bent  back  and  broken  to  mean 
(of  optical  rays)  that  they  are  reflected  and  refracted ;  but  then 
we  should  have  no  means  of  speaking  of  the  angles  of  reflection 
and  refraction,  of  the  refractive  indices,  and  the  like. 

Thus  one  of  the  advantages  of  going  to  the  Greek  and  Latin 
languages  for  the  origin  of  our  scientific  terms  is,  that  in  this  way 
we  obtain  words  which  admit  of  the  formation  of  adjectives  and 
abstract  terms,  of  composition,  and  of  other  inflexions.  Another 
advantage  of  such  an  origin  is,  that  such  terms,  if  well  selected, 
are  readily  understood  over  the  whole  lettered  world.  For  this 
reason,  the  descriptive  language  of  science,  of  botany  for  instance, 
has  been,  for  the  most  part,  taken  from  the  Latin ;  many  of  the 
terms  of  the  mathematical  and  chemical  sciences  have  been 
derived  from  the  Greek ;  and  when  occasion  occurs  to  construct 
a  new  term,  it  is  generally  to  that  language"  that  recourse  is  had. 
The  advantage  of  such  terms  is,  as  has  already  been  intimated, 
that  they  constitute  an  universal  language,  by  means  of  which 
cultivated  persons  in  every  country  may  convey  to  each  other 
their  ideas  without  the  need  of  translation. 

On  the  other  hand,  the  advantage  of  indigenous  terms  is, 
that  so  far  as  the  language  extends,  they  are  intelligible  much 
more  clearly  and  vividly  than  those  borrowed  from  any  other 
source,  as  well  as  more  easily  manageable  in  the  construction  of 
sentences.  In  the  descriptive  language  of  botany,  for  example, 
in  an  English  work,  the  terms  drooping,  nodding,  one-sided, 
twining,  straggling,  appear  better  than  cernuous,  nutant,  secund, 
wlubile,  divaricate.  For  though  the  latter  terms  may  by  habit 
become  as  intelligible  as  the  former,  they  cannot  become  more  so 
to  any  readers ;  and  to  most  English  readers  they  will  give  a  far 
less  distinct  impression. 

2.  Since  the  advantage  of  indigenous  over  learned  terms,  or 
the  contrary,  depends  upon  the  balance  of  the  capacity  of  inflexion 
and  composition  on  the  one  hand,  against  a  ready  and  clear  signi- 
ficance on  the  other,  it  is  evident  that  the  employment  of  scientific 
terms  of  the  one  class  or  of  the  other  may  very  properly  be  ex- 
tremely different  in  different  languages.  The  German  possesses 
in  a  very  eminent  degree  that  power  of  composition  and  derivation, 


XCV111  APHORISMS   CONCERNING 

which  in  English  can  hardly  be  exercised  at  all,  in  a  formal 
manner.  Hence  German  scientific  writers  use  native  terms  to  a 
far  greater  extent  than  do  our  own  authors.  The  descriptive 
terminology  of  botany,  and  even  the  systematic  nomenclature  of 
chemistry,  are  represented  by  the  Germans  by  means  of  German 
roots  and  inflexions.  Thus  the  description  of  Potentilla  anserina, 
in  English  botanists,  is  that  it  has  Leaves  interruptedly  pinnate, 
serrate,  silky,  stem  creeping,  stalks  axillar,  one-flowered.  Here 
we  have  words  of  Saxon  and  Latin  origin  mingled  pretty  equally. 
But  the  German  description  is  entirely  Teutonic.  Die  Blume  in 
Achsel ;  die  Blatter  unterbrochen  gefiedert,  die  Bldttchen  scharf 
gesagt,  die  Stdmme  kriechend,  die  Bluthenstiele  eiiiblumig.  We 
could  imitate  this  in  our  own  language,  by  saying  brokenly- 
feathered,  sharp-sawed ;  by  using  threed  for  ternate,  as  the  Ger- 
mans employ  gedreit ;  by  saying  fingered- feathered  for  digitato- 
pinnate,  and  the  like.  But  the  habit  which  we  have,  in  common 
as  well  as  in  scientific  language,  of  borrowing  words  from  the 
Latin  for  new  cases,  would  make  such  usages  seem  very  harsh 
and  pedantic. 

We  may  add  that,  in  consequence  of  these  different  practices 
in  the  two  languages,  it  is  a  common  habit  of  the  German  reader 
to  impose  a  scientific  definiteness  upon  a  common  word,  such  as 
our  Fifth  Aphorism  requires ;  whereas  the  English  reader  expects 
rather  that  a  word  which  is  to  have  a  technical  sense  shall  be 
derived  from  the  learned  languages.  Die  Kelch  and  die  Blume 
(the  cup  and  the  flower)  easily  assume  the  technical  meaning  of 
calyx  and  corolla ;  die  griffel  (the  pencil)  becomes  the  pistil ; 
and  a  name  is  easily  found  for  the  pollen,  the  anthers,  and  the 
stamens,  by  calling  them  the  dust,  the  dust-cases,  and  the  dust- 
threads  (der  staub,  die  staub-beutel  or  staub-fdcher,  and  die  staub- 
fdden).  This  was  formerly  done  in  English  to  a  greater  extent 
than  is  now  possible  without  confusion  and  pedantry.  Thus,  in 
Grew's  book  on  the  Anatomy  of  Plants,  the  calyx  is  called  the 
impalement,  and  the  sepals  the  impalers ;  the  petals  are  called 
the  leaves  of  the  flower ;  the  stamens  with  their  anthers  are  the 
seminiform  attire.  But  the  English  language,  as  to  such  mat- 
ters, is  now  less  flexible  than  it  then  was ;  partly  in  conse- 


THE   LANGUAGE   OF    SCIENCE.  XC1X 

quence  of  having  adopted  the  Linnsean  terminology  almost  entire, 
without  any  attempt  to  naturalise  it.  For  any  attempt  at  idio- 
matic description  would  interfere  with  the  scientific  language  now 
generally  received  in  this  country.  In  Germany,  on  the  other 
hand,  those  who  wrote  upon  science  in  their  own  language  imi- 
tated the  Latin  words  which  they  found  in  foreign  writers, 
instead  of  transferring  new  roots  into  their  own  language.  Thus 
the  numerator  and  denominator  of  a  fraction  they  called  the  namer 
and  the  counter  (iienner  and  zahler).  This  course  they  pursued 
even  where  the  expression  was  erroneous.  Thus  that  portion 
of  the  intestines  which  ancient  anatomists  called  duodenum, 
because  they  falsely  estimated  its  length  at  twelve  inches,  the 
Germans  also  term  zwolffingerdarm  (twelve-inch-gut),  though 
this  intestine  in  a  whale  is  twenty  feet  long,  and  in  a  frog  not 
above  twenty  lines.  As  another  example  of  this  process  in  Ger- 
man, we  may  take  the  word  muttersackbauchblatte,  the  uterine 
peritonaeum. 

It  is  a  remarkable  evidence  of  this  formative  power  of  the 
German  language,  that  it  should  have  been  able  to  produce 
an  imitation  of  the  systematic  chemical  nomenclature  of  the 
French  school,  so  complete,  that  it  is  used  in  Germany  as  fami- 
liarly as  the  original  system  is  in  France  and  England.  Thus 
Oxygen  and  Hydrogen  are  Sauerstoff  and  Wafferstoff;  Azote  is 
Stickstoff  (suffocating  matter)  ;  Sulphuric  and  Sulphurous  Acid 
are  Schwefel-saure  and  Schwefelichte-sdure.  The  Sulphate  and  Sul- 
phite of  Baryta,  and  Sulphuret  of  Baryum,  are  Schwefel-saure 
Barijterde,  Schwefelichte-saure  Baryterde,  and  Schwefel-baryum. 
Carbonate  of  Iron  is  Kohlen-sdures  Eisenoxydul,  and  we  may 
observe  that,  in  such  cases,  the  German  name  is  much  more  agree- 
able to  anology  than  the  English  one;  for  the  Protoxide  of 
Iron,  and  not  the  Iron  itself,  is  the  base  of  the  salt.  And  the 
German  language  has  not  only  thus  imitated  the  established 
nomenclature  of  chemistry,  but  has  shown  itself  capable  of  sup- 
plying new  forms  to  meet  the  demands  which  the  progress  of 
theory  occasions.  Tims  the  Hydracids  are  Wasserstoff-sduren ; 
and  of  these,  the  Hyclriodic  Acid  is  lodwasserstoff-saure,  and  so 
of  the  rest.  In  like  manner,  the  translator  of  Berzelius  has  found 


C  APHORISMS  CONCERNING 

German  names  for  the  sulpho-salts  of  that  chemist ;  thus  he  has 
Wasserstoffschwefliges  Schwef el-lithium,  which  would  be  (if  we 
were  to  adopt  his  theoretical  view,)  hydro-sulphuret  of  sulphuret 
of  lithium  :  and  a  like  nomenclature  for  all  other  similar  cases. 

3.  In   English  we  have  no  power  of  imitating  this  process, 
and  must  take  our  technical  phrases  from  some  more  flexible 
language,  and  generally  from  the  Latin  or  Greek.     We  are  indeed 
so  much  accustomed  to  do  this,  that  except  a  word  has  its  origin 
in  one  of  these  languages,  it  hardly  seems  to  us  a  technical  term ; 
and  thus  by  employing  indigenous  terms,  even  descriptive  ones, 
we  may,  perhaps,  lose  in  precision  more  than  we  gain  in  the  vivid- 
ness of  the  impression.     Perhaps  it  may  be  better  to  say  cuneate, 
lunate,  hastate,  sagittate,   reniform,   than  wedge-shaped,  crescent- 
shaped,  halbert-headed,  arrow -headed,  kidney-shaped.     Ringent  and 
personate  are  better  than  any  English  words  which  we  could  sub- 
stitute for  them  ;  labiate  is  more  precise  than  lipped  would  readily 
become.      Urceolate,  trochlear,   are  more  compact  than  pitcher- 
shaped,    pulley  -  shaped ;    and    infundibuliform,    hypocrateriform, 
though  long  words,  are  not  more  inconvenient  than  funnel-shaped 
and  saher-shaped.     In  the  same  way  it  is  better  to  speak  (with 
Dr.  Prichard*,)  of  repent  and  progressive  animals,  than  of  creeping 
and  progressive  :  the  two  Latin  terms  make  a  better  pair  of  cor- 
relatives. 

4.  But  wherever  we  may  draw  the  line  between  the  proper  use 
of  English  and  Latin  terms  in  descriptive  phraseology,  we  shall 
find  it  advisable  to  borrow  almost  all  other  technical  terms  from 
the  learned  languages.     We  have  seen  this  in  considering  the 
new  terms  introduced  into  various  sciences  in  virtue  of  our  Ninth 
Maxim.     We  may  add  as  further  examples  the  names  of  the 
various   animals  of  which  a  knowledge  has  been  acquired  from 
the  remains  of  them  which  exist  in  various  strata,  and  which 
have  been  reconstructed  by  Cuvier  and  his  successors.     Such  are 
the  Palceotlierium,   the   Anoplotherium,   the   Megatherium,   the 
Dinotherium,  the  Chirotherium,  the  Megalichthys,  the  Mastodon, 
the  Ichthyosaurus,  the  Plesiosaurus,  the  Pterodactylus.     To  these 
others  are  every  year  added ;  as,  for  instance,  very  recently,  the 

*  Researches,  p.  69. 


THE  LANGUAGE  OF  SCIENCE.  ci 

Toxodon,  Zeuglodon,  and  Phascolotherium  of  Mr.  Owen,  and  the 
Thylacotherium  of  M.  Valenciennes.  The  names  of  species,  as  well 
as  of  genera,  are  thus  formed  from  the  Greek :  as  the  Plesiosau- 
rus  dolickodeirus,  (long-necked),  Ichthyosaurus  platyodon  (broad- 
toothed),  the  Irish  elk,  termed  Cervus  megaceros  (large-horned). 
But  the  descriptive  specific  names  are  also  taken  from  the  Latin, 
as  Plesiosaurus  brevirottrif,  longirostris,  crassirostris ;  besides 
which  there  are  arbitrary  specific  names,  which  we  do  not  here 
consider.  These  names  being  all  constructed  at  a  period  when 
naturalists  were  familiar  with  an  artificial  system,  the  standard 
language  of  which  is  Latin,  have  not  been  taken  from  modern 
language.  But  the  names  of  living  animals,  and  even  of  their 
classes,  long  ago  formed  in  the  common  language  of  men,  have 
been  in  part  adopted  in  the  systems  of  naturalists,  agreeably  to 
Aphorism  Third.  Hence  the  language  of  systems  in  natural 
history  is  mixed  of  ancient  and  modern  languages.  Thus  Cuvier's 
divisions  of  the  vertebrated  animals  are  Mammiferes  (Latin), 
Oiseaux,  Beptiles,  Poissons ;  Bimanes,  Qtiadrumanes,  Carnassieres, 
Rongeurs,  Pacliydermes  (Greek),  Euminans  (Latin),  Cetaces 
(Latin).  In  the  subordinate  divisions  the  distribution  being 
more  novel,  the  names  are  less  idiomatic :  thus  the  kinds  of  Rep- 
tiles are  Cheloniens,  Sauriens,  Ophidiens,  Batriciens,  all  which 
are  of  Greek  origin.  In  like  manner,  Fish  are  divided  into 
Chondropterygiens,  Malacopterygiens,  Acanihopterygiens.  The 
unvertebrated  animals  are  Mollusques  or  Animaux  articules,  and 
Animaux  ray  ounces ;  and  the  former  are  divided  into  six  classes, 
according  to  the  position  of  their  foot ;  namely,  Cephalopodes, 
Pteropodes,  Gasteropodes,  Acephales,  Brachiopodes,  Cirrhopodes. 

In  transferring  these  terms  into  English,  when  the  term  is 
new  in  French  as  well  as  English,  we  have  little  difficulty ;  for 
we  may  take  nearly  the  same  liberties  in  English  which  are 
taken  in  French;  and  hence  we  may  say  mammifers  (rather 
mammals),  cetaceans  or  cetaces,  batracians  (rather  latrachians), 
using  the  words  as  substantives.  But  in  other  cases  we  must  go 
back  to  the  Latin :  thus  we  say  radiate  animals,  or  radiata 
(rather  radials),  for  rayonnees.  These  changes,  however,  rather 
refer  to  another  Aphorism. 


Cli  APHORISMS  CONCERNING 

5.  When  new  mineral  species  have  been  established  in  recent 
times,  they  have  generally  had  arbitrary  names  assigned  to  them, 
derived  from  some  person  or  places.     In  some  instances,  however, 
descriptive  names  have  been  selected  ;    and  then  these  have  been 
generally  taken  from  the  Greek,  as  Auglte,  Stilbite,  Diaspore, 
Dichrolte,  Dioptase.     Several  of  these  Greek  names  imposed  by 
Haiiy,  refer  to  some  circumstances,  often  fancifully  selected,  in 
his  view  of  the  crystallization  of  the  substance,  as  Epidote,  Peri- 
dote,  Pleonast.     Similar  terms  of  Greek  origin  have  been  intro- 
duced by  others,  as  Orthite,  Anorthite,  Periklin.     Greek  names 
founded   on   casual   circumstances   are   less   to   be   commended. 
Berzelius  has  termed  a  mineral  Eschynite,  from  aiGyyvri,  shame, 
because  it  is,  he  conceives,  a  shame  for  chemists  not  to  have  sepa- 
rated its  elements  more  distinctly  than  they  did  at  first. 

6.  In  Botany,  the  old  names  of  genera  of  Greek  origin  are 
very  numerous,  and  many  of  them  are  descriptive,  as  Glycyrhiza 
(<y\vicvs&\\&  pl£a,  sweet  root)  liquorice,  Rhododendron  (rose  tree), 
Hcematoxylon  (bloody  wood),   Chrysocoma  (golden  hair),  Alope- 
curus  (fox  tail),  and  many  more.     In  like   manner  there   are 
names  which  derive  a  descriptive  significance  from  the  Latin, 
either  adjectives,  as  Impatiens,  Gloriosa,  Sagittaria,  or  substan- 
tives irregularly  formed,  as  Tussilago  (atussis  domatione),  Urtica 
(ab  urendo  tactu),  Salsola  (a  salsedine).     But  these,  though  good 
names  when  they  are  established  by  tradition,  are  hardly  to  be 
imitated  in  naming  new  plants.     In  most  instances,  when  this  is 
to  be  done,  arbitrary  or  local  names  have  been  selected,  as  Stre- 
litzia. 

7.  In  Chemistry,  new  substances  have   of  late  had   names 
assigned  them  from  Greek  roots,  as  Iodine,  from  its  violet  colour, 
Chlorine  from  its  green  colour.     In  like  manner  fluorine  has  by 
the   French  chemists  been  called  Phthor,  from  its  destructive 
properties.      So  the  new   metals,    Chrome,   Rhodium,   Iridium, 
Osmium,  had  names  of  Greek  derivation  descriptive  of  their  pro- 
perties.   Some  such  terms,  however,  were  borrowed  from  localities, 
as  Strontia,   Yttria,  the  names  of  new  earths.     Others  have  a 
mixed  origin,  as  Pyrogallic,  Pyroacetic,  and  Pyroligneous  Spirit. 
In  some  cases  the  deviation  has  been  extravagantly  capricious. 


THE  LANGUAGE  OF  SCIENCE.  Clll 

Thus  in  the  process  for  making  Pyrogallic  Acid,  a  certain  sub- 
stance is  left  behind,  from  which  M.  Braconnot  extracted  an  acid 
which  he  called  Ellagic  Acid,  framing  the  root  of  the  name  by 
reading  the  word  Galle  backwards. 

The  new  laws  which  the  study  of  electro-chemistry  brought 
into  view,  required  a  new  terminology  to  express  their  conditions : 
and  in  this  case,  as  we  have  observed  in  speaking  of  the  Twelfth 
Maxim,  arbitrary  words  are  less  suitable.  Mr.  Faraday  very 
properly  borrowed  from  the  Greek  his  terms  Electrolyte,  Electrode, 
Anode,  Cathode,  An'ion,  Catk'ion,  Dilectric.  In  the  mechanico- 
chemical  and  mechanical  sciences,  however,  new  terms  are  less 
copiously  required  than  in  the  sciences  of  classification,  and  when 
they  are  needed,  they  are  generally  determined  by  analogy  from 
existing  terms.  Thermo-electricity  and  Electro-dynamics  were  terms 
which  very  naturally  offered  themselves ;  Nobili's  thermo-mul- 
tiplier,  Snow  Harris's  unit-jar,  were  almost  equally  obvious 
names.  In  such  cases,  it  is  generally  possible  to  construct  terms 
both  compendious  and  descriptive,  without  introducing  any  new 
radical  words. 

8.  The  subject  of  crystallography  has  inevitably  given  rise  to 
many  new  terms,  since  it  brings  under  our  notice  a  great  number 
of  new  relations  of  a  very  definite  but  very  complex  form. 
Haiiy  attempted  to  find  names  for  all  the  leading  varieties  of 
crystals,  and  for  this  purpose  introduced  a  great  number  of  new 
terms,  founded  on  various  analogies  and  allusions.  Thus  the 
forms  of  calc-spar  are  termed  by  him  primitive,  equia&e,  inverse, 
metastatique,  contrastante,  imitable,  birhomboidale,  prismatique, 
apophane,  uniternaire,  bisunitaire,  dodecaedre,  contracted,  dilatce, 
sexduodecimale,  bisalterne,  binoternaire,  and  many  others.  The 
want  of  uniformity  in  the  origin  and  scheme  of  these  denomina- 
tions would  be  no  valid  objection  to  them,  if  any  general  truth 
could  be  expressed  by  means  of  them  :  but  the  fact  is,  that  there 
is  no  definite  distinction  of  these  forms.  They  pass  into  each 
other  by  insensible  gradations,  and  the  optical  and  physical  pro- 
perties which  they  possess  are  common  to  all  of  them.  And  as 
a  mere  enunciation  of  laws  of  form,  this  terminology  is  insuffi- 
cient. Thus  it  does  not  at  all  convey  the  relation  between  the 


CIV  APHORISMS  CONCERNING 

bisalterne  and  the  binoternaire,  the  former  being  a  combination  of 
the  metastatique  with  the  prismatique,  the  latter  of  the  metastique 
with  the  contrastante :  again,  the  contrastante,  the  mixte,  the 
cuboide,  the  contractee,  the  dilatee,  all  contain  faces  generated  by 
a  common  law,  the  index  being  respectively  altered  so  as  to  be  in 
these  cases,  3,  f ,  •£ ,  •£- ,  -§- ;  and  this,  which  is  the  most  important  geo- 
metrical relation  of  these  forms,  is  not  at  all  recorded  or  indicated 
by  the  nomenclature.  The  fact  is,  that  it  is  probably  impossible, 
the  subject  of  crystallography  having  become  so  complex  as  it 
now  is,  to  devise  a  system  of  names  which  shall  express  the  rela- 
tions of  form.  Numerical  symbols,  such  as  those  of  Weiss  or 
Naumann,  or  Professor  Miller,  are  the  proper  ways  of  expressing 
these  relations,  and  are  the  only  good  crystallographic  terminology 
for  cases  in  detail. 

The  terms  used  in  expressing  crystallographic  laws  have 
been  for  the  most  part  taken  from  the  Greek  by  all  writers  except 
some  of  the  Germans.  These,  we  have  already  stated,  have 
constructed  terms  in  their  own  language,  as  zwei-und-ein  gliedrig, 
and  the  like. 

In  Optics  we  have  some  new  terms  connected  with  crystal- 
line laws,  as  uniaxal  and  biaxal  crystals,  optical  axes,  which 
offered  themselves  without  any  effort  on  the  part  of  the  discover- 
ers. In  the  whole  history  of  the  undulatory  theory,  very  few 
innovations  in  language  were  found  necessary,  except  to  fix  the 
sense  of  a  few  phrases,  as  plane-polarized  light  in  opposition  to 
circularly -polarized,  and  the  like. 

This  is  still  more  the  case  in  Mechanics,  Astronomy,  and  pure 
mathematics.  In  these  sciences,  several  of  the  primary  stages  of 
generalization  being  already  passed  over,  when  any  new  steps  are 
made,  we  have  before  us  some  analogy  by  which  we  may  frame 
our  new  terms.  Thus  when  the  plane  of  maximum  areas  was 
discovered,  it  had  not  some  new  arbitrary  denomination  assigned 
it,  but  the  name  which  obviously  described  it  was  fixed  as  a 
technical  name. 

The  result  of  this  survey  of  the  scientific  terms  of  recent 
formation  seems  to  be  this; — that  indigenous  terms  may  be 
employed  in  the  descriptions  of  facts  and  phenomena  as  they  at 


THE   LANGUAGE   OF    SCIENCE.  CV 

first  present  themselves ;  and  in  the  first  induction  from  these ; 
but  that  when  we  come  to  generalize  and  theorize,  terms  borrowed 
from  the  learned  languages  are  more  readily  fixed  and  made 
definite,  and  are  also  more  easily  connected  with  derivatives. 
Our  native  terms  are  more  impressive,  and  at  first  more  intelli- 
gible ;  but  they  may  wander  from  their  scientific  meaning,  and 
are  capable  of  little  inflexion.  Words  of  classical  origin  are 
precise  to  the  careful  student,  and  capable  of  expressing,  by  their 
inflexions,  the  relations  of  general  ideas ;  but  they  are  unintelli- 
gible, even  to  the  learned  man,  without  express  definition,  and 
convey  instruction  only  through  an  artificial  and  rare  habit  of 
thought. 

Since  in  the  balance  between  words  of  domestic  and  of  foreign 
origin  so  much  depends  upon  the  possibility  of  inflexion  and 
derivation,  I  shall  consider  a  little  more  closely  what  are  the 
limits  and  considerations  which  we  have  to  take  into  account  in 
reference  to  that  subject. 

APHORISM  XVI. 

In  the  composition  and  inflexion  of  technical  terms,  philological 
analogies  are  to  be  preserved  if  possible,  but  modified  according 
to  scientific  convenience. 

IN  the  language  employed  or  proposed  by  writers  upon  sub- 
jects of  science,  many  combinations  and  forms  of  derivation  occur, 
which  would  be  rejected  and  condemned  by  those  who  are  careful 
of  the  purity  and  correctness  of  language.  Such  anomalies  are 
to  be  avoided  as  much  as  possible  ;  but  it  is  impossible  to  escape 
them  altogether,  if  we  are  to  have  a  scientific  language  which 
has  any  chance  of  being  received  into  general  use.  It  is  better 
to  admit  compounds  which  are  not  philologically  correct,  than 
to  invent  many  new  words,  all  strange  to  the  readers  for  whom 
they  are  intended :  and  in  writing  on  science  in  our  own  lan- 
guage, it  is  not  possible  to  avoid  making  additions  to  the  voca- 
bulary of  common  life;  since  science  requires  exact  names  for 
many  things  which  common  language  has  not  named.  And 

VOL.  I.  h 


CV1  APHORISMS   CONCERNING 

although  these  new  names  should,  as  much  as  possible,  be 
constructed  in  conformity  with  the  analogies  of  the  language, 
such  extensions  of  analogy  can  hardly  sound,  to  the  gram- 
marian's ear,  otherwise  than  as  solecisms.  But,  as  our  maxim 
indicates,  the  analogy  of  science  is  of  more  weight  with  us 
than  the  analogy  of  language :  and  although  anomalies  in  our 
phraseology  should  be  avoided  as  much  as  possible,  innovations 
must  be  permitted  wherever  a  scientific  language,  easy  to  acquire, 
and  convenient  to  use,  is  unattainable  without  them. 

I  shall  proceed  to  mention  some  of  the  transgressions  of  strict 
philological  rules,  and  some  of  the  extensions  of  grammatical  forms, 
which  the  above  conditions  appear  to  render  necessary. 

I.  The  combination  of  different  languages  in  the  derivation 
of  words,  though  to  be  avoided  in  general,  is  in  some  cases  ad- 
missible. 

Such  words  are  condemned  by  Quintilian  and  other  gramma- 
rians, under  the  name  of  hybrids,  or  things  of  a  mixed  race  ;  as 
biclinium,  from  bis  and  K\lvri ;  epitogium,  from  eVl  and  toga. 
Nor  are  such  terms  to  be  unnecessarily  introduced  in  science. 
Whenever  a  homogeneous  word  can  be  formed  and  adopted  with 
the  same  ease  and  convenience  as  a  hybrid,  it  is  to  be  preferred. 
Hence  we  must  have  ichthyology,  not  piscology,  entomology,  not 
insectology,  insectivorous  not  insectophagous.  In  like  manner,  it 
would  be  better  to  say  unoculus  than  monoculus,  though  the 
latter  has  the  sanction  of  Linnaeus,  who  was  a  purist  in  such 
matters.  Dre  Turner,  in  his  Chemistry,  speaks  of  protoxides  and 
binoxides,  which  combination  violates  the  rule  for  making  the 
materials  of  our  terms  as  homogeneous  as  possible ;  protoxide 
and  deutoxide  would  be  preferable,  both  on  this  and  on  other 
accounts. 

Yet  this  rule  admits  of  exceptions.  Mineralogy,  with  its 
Greek  termination,  has  for  its  root  minera,  a  medieval  Latin  word 
of  Teutonic  origin,  and  is  preferable  to  oryctology.  Terminology 
appears  to  be  better  than  glossology :  which  according  to  its  deri- 
vation would  be  rather  the  science  of  language  in  general  than  of 
technical  terms ;  and  horology,  from  opos,  a  term,  would  not  be 
immediately  intelligible,  even  to  Greek  scholars  ;  and  is  already 


THE    LANGUAGE   OF   SCIENCE.  CVii 

employed  to  indicate  the  science  which  treats  of  horologes,  or 
time-pieces. 

Indeed,  the  English  reader  is  become  quite  familiar  with  the 
termination  ology,  the  names  of  a  large  number  of  branches 
of  science  and  learning  having  that  form.  This  termination 
is  at  present  rather  apprehended  as  a  formative  affix  in  our 
own  language,  indicating  a  science,  than  as  an  element  borrowed 
from  a  foreign  language.  Hence,  when  it  is  difficult  or  imposs- 
ible to  find  a  Greek  term  which  clearly  designates  the  subject  of  a 
science,  it  is  allowable  to  employ  some  other,  as  in  Tidology,  the 
doctrine  of  the  tides. 

The  same  remark  applies  to  some  other  Greek  elements  of 
scientific  words :  they  are  so  familiar  to  us  that  in  composition 
they  are  almost  used  as  part  of  our  own  language.  This  natu- 
ralization has  taken  place  very  decidedly  in  the  element  arch, 
(dpxbs,  a  leader,)  as  we  see  in  archbishop,  archduke.  It  is  effected 
in  a  great  degree  for  the  preposition  anti :  thus  we  speak  of  anti- 
slavery  societies,  anti-reformers,  anti-bilious,  or  anti-acid,  medi- 
cines, without  being  conscious  of  any  anomaly.  The  same  is  the 
ease  with  the  Latin  preposition  pro?  or  pre,  as  appears  from  such 
words  as  pre-engage,  pre-arrange,  pre-judge,  pre-paid ;  and  in 
some  measure  with  pro,  for  in  colloquial  language  we  speak  of 
pro-catholics  and  anti-catholics.  Also  the  preposition  ante  is  simi- 
larly used,  asante-nicene  fathers.  The  preposition  co,  abbreviated 
from  con,  and  implying  things  to  be  simultaneous  or  connected, 
is  firmly  established  as  part  of  the  language,  as  we  see  in  coexist, 
coheir,  coordinate ;  hence  I  have  called  those  lines  cotidal  lines 
which  pass  through  places  where  the  high  water  of  the  tide 
occurs  simultaneously. 

2.  As  in  the  course  of  the  mixture  by  which  our  language 
has  been  formed,  we  have  thus  lost  all  habitual  consciousness  of 
the  difference  of  its  ingredients  (Greek,  Latin,  Norman,  French, 
and  Anglo-Saxon)  :  we  have  also  ceased  to  confine  to  each  ingre- 
dient the  mode  of  grammatical  inflexion  which  originally  belonged 
to  it.  Thus  the  termination  ive  belongs  peculiarly  to  Latin 
adjectives,  yet  we  say  sportive,  talkative.  In  like  manner,  able  is 
added  to  words  which  are  not  Latin,  as  eatable,  drinkable^  piti- 


CViii  APHORISMS   CONCERNING 

able,  enviable.  Also  the  termination  al  and  ical  are  used  with 
various  roots,  as  loyal,  royal,  farcical,  whimsical;  hence  we  may 
make  the  adjective  tidal  from  tide.  This  ending,  al,  is  also 
added  to  abstract  terms  in  ion,  as  occasional,  provisional,  inten- 
tional, national;  hence  we  may,  if  necessary,  use  such  words 
as  educational,  terminational.  The  ending  ic  appears  to  be  suited 
to  proper  names,  as  Pindaric,  Socratic,  Platonic ;  hence  it  may 
be  used  when  scientific  words  are  derived  from  proper  names,  as 
Voltaic  or  Galvanic  electricity :  to  which  I  have  proposed  to  add 
Franklinic. 

In  adopting  scientific  adjectives  from  the  Latin,  we  have  not 
much  room  for  hesitation ;  for,  in  such  cases,  the  habits  of  deri- 
vation from  that  language  into  our  own  are  very  constant ;  ivus 
becomes  ive,  as  decursive ;  inus  becomes  ine,  as  in  ferine ;  atus 
becomes  ate,  as  hastate;  and  us  often  becomes  ous,  as  rufous;  aris 
becomes  ary,  as  axillary;  ens  becomes  ent,  as  ringent.  And  in 
adopting  into  our  language,  as  scientific  terms,  words  which  in 
another  language,  the  French  for  instance,  have  a  Latin  origin 
familiar  to  us,  we  cannot  do  better  than  form  them  as  if  they 
were  derived  directly  from  the  Latin.  Hence  the  French  adjec- 
tives cetace,  crustace,  testace,  may  become  either  cetaceous,  crusta- 
ceous,  testaceous,  according  to  the  analogy  of  farinaceous,  preda- 
ceous,  or  else  cetacean,  crustacean,  testacean,  imitating  the  form 
of  patrician.  Since,  as  I  shall  soon  have  to  notice,  we  require 
substantives  as  well  as  adjectives  from  these  words,  we  must,  at 
least  for  that  use,  take  the  forms  last  suggested. 

In  pursuance  of  the  same  remark,  rongeur  becomes  rodent, 
and  edente  would  become  edentate ;  but  that  this  word  is  rejected 
on  another  account :  the  adjectives  bimane  and  guadrumane  are 
bimanous  and  quadrumanous. 

3.  There  is  not  much  difficulty  in  thus  forming  adjectives : 
but  the  purposes  of  Natural  History  require  that  we  should  have 
substantive  words  corresponding  to  these  adjectives;  and  these 
cannot  be  obtained  without  some  extension  of  the  analogies  of  our 
language.  We  cannot  in  general  use  adjectives  or  participles  as 
singular  substantives.  The  happy  or  the  doomed  would,  according 
to  good  English  usage,  signify  those  who  are  happy  and  those 


THE    LANGUAGE    OF    SCIENCE.  cix 

who  are  doomed.  Hence  we  could  not  speak  of  a  particular 
scaled  animal  as  the  squamate,  and  still  less  could  we  call  any  such 
animal  a  squamate,  or  speak  of  squamates  in  the  plural.  Some 
of  the  forms  of  our  adjectives,  however,  do  admit  of  this  substan- 
tive use.  Thus  we  talk  of  Europeans,  plebeians,  republicans ;  of 
divines  and  masculines ;  of  the  ultramontanes ;  of  mordants  and 
brilliants ;  of  abstergents  and  emollients ;  of  mercenaries  and  tribu- 
taries; of  animals,  manuals,  and  officials;  of  dissuasives  and 
motives.  We  cannot  generally  use  in  this  way  adjectives  in  ous, 
nor  in  ate  (though  reprobates  is  an  exception),  nor  English  par- 
ticiples, nor  adjectives  in  which  there  is  no  termination  imitating 
the  Latin,  as  happy,  good.  Hence,  if  we  have,  for  purposes  of 
science,  to  convert  adjectives  into  substantives,  we  ought  to 
follow  the  form  of  examples  like  these,  in  which  it  has  already 
appeared  in  fact,  that  such  usage,  though  an  innovation  at  first, 
may  ultimately  become  a  received  part  of  the  language. 

By  attention  to  this  rule  we  may  judge  what  expressions  to 
select  in  cases  where  substantives  are  needed.  I  will  take  as  an 
example  the  division  of  the  mammalian  animals  into  orders. 
These  orders,  according  to  Cuvier,  are  Bimanes,  Quadrumanes, 
Carnassiers,  Rongeurs,  Edentes,  Ruminans,  Pachydermes,  Cetaces. 
Bimanes,  Quadrumanes,  Rodents,  Ruminants,  are  admissible  as 
English  substantives  on  the  grounds  just  stated.  Cetaceous 
could  not  be  used  substantively ;  but  Cetacean  in  such  a  usage  is 
sufficiently  countenanced  by  such  cases  as  we  have  mentioned, 
patrician,  &c. ;  hence  we  adopt  this  form.  We  have  no  English 
word  equivalent  to  the  French  Carnassiers :  the  English  trans- 
lator of  Cuvier  has  not  provided  English  words  for  his  technical 
terms ;  but  has  formed  a  Latin  word,  Carnaria,  to  represent  the 
French  terms.  From  this  we  might  readily  form  Carnaries ; 
but  it  appears  much  better  to  take  the  Linnsean  name  Ferce  as 
our  root,  from  which  we  may  take  Ferine,  substantive  as  well  as 
adjective ;  and  hence  we  call  this  order  Ferines.  The  word  for 
which  it  is  most  difficult  to  provide  a  proper  representation,  is 
Edente,  Edentata :  for,  as  we  have  said,  it  would  be  very  harsh  to 
speak  of  the  order  as  the  Edentates ;  and  if  we  were  to  abbreviate 
the  word  into  edent,  we  should  suggest  a  false  analogy  with 


CX  APHORISMS   CONCERNING 

rodent,  for  as  rodent  is  quod  rodit,  that  which  gnaws,  edent  wouM 
be  quod  edit,  that  which  eats.  And  even  if  we  were  to  take 
edent  as  a  substantive,  we  could  hardly  use  it  as  an  adjective  :- 
we  should  still  have  to  say,  for  example,  the  edentate  form  of 
head.  For  these  reasons  it  appears  best  to  alter  the  form  of  the 
word,  and  to  call  the  order  the  Edentals,  which  is  quite  allow- 
able, both  as  adjective  and  substantive. 

There  are  several  other  words  in  ate  about  which  there  is  the 
same  difficulty  in  providing  substantive  forms.  Are  we  to  speak 
of  Vertebrates  ?  or  would  it  not  be  better,  in  agreement  with  what 
has  been  said  above,  to  call  these  Vertebrals,  and  the  opposite 
class  Invertebrate  ? 

There  are  similar  difficulties  with  regard  to  the  names  of  sub- 
ordinate portions  of  zoological  classification ;  thus  the  Ferines  are 
divided  by  Cuvier  into  Cheiropteres,  Insectiwres,  Carnivores ; 
and  these  latter  into  Plantigrades,  Digitigrades,  Amphibies,  Mar- 
mpiaux.  There  is  not  any  great  harshness  in  naturalizing  these 
substantives  as  Chiropters,  Insectivores,  Carnivores,  Plantigrades, 
Digitigrades,  Amphibians,  and  Marsupials.  The  words  Carni- 
vores and  Insectivores  are  better,  because  of  more  familiar  origin, 
than  Greek  terms;  otherwise  we  might,  if  necessary,  speak  of 
Zoophagans  and  Entomophagans. 

It  is  only  with  certain  familiar  adjectival  terminations,  as  ous 
and  ate,  that  there  is  a  difficulty  in  using  the  word  as  substantive. 
When  this  can  be  avoided,  we  readily  accept  the  new  word,  as 
Pachyderms,  and  in  like  manner  MollusJcs. 

If  we  examine  the  names  of  the  Orders  of  Birds,  we  find  that 
they  are  in  Latin,  Predator es  or  Accipitres,  Passer es,  Scansores, 
Easores  or  Gallinw,  Grallatores,  Palmipedes  and  Anseres :  Cuvier's 
Orders  are,  Oiseaux  de  Proie,  Passereaux,  Grimpeurs,  Gallina- 
ces,  Echassiers,  Palmipedes.  These  may  be  englished  conveni- 
ently as  Predators,  Passerines,  Scansors,  Gallinaceans,  (rather  than 
Rasors,)  Grallators,  Palmipedans.  Scansors,  Grallators,&ndiRasor$ 
are  better,  as  technical  terms,  than  Climbers,  Waders,  and  Scratch- 
ers.  We  might  venture  to  anglicize  the  terminations  of  the 
names  which  Cuvier  gives  to  the  divisions  of  these  Orders  :  thus 
the  Predators  are  the  Diurnals  and  the  Nocturnals ;  the  Passer- 


THE  LANGUAGE  OF  SCIENCE.  Cxi 

ines  are  the  Dentirostres,  the  Fissirostres,  the  Conirostres,  the 
Tenuirostres,  and  the  Syndactyls :  the  word  lustre  showing  that 
the  former  termination  is  allowable.  The  Scansors  are  not  sub- 
divided, nor  are  the  Gallinaceans.  The  Grallators  are  Pressirostres, 
Cultrirostres,  and  Macrodactyls.  The  Palmipedans  are  the  Plung- 
ers, the  Longipens,  the  Totipalmes  and  the  Lamellirostres. 

The  next  class  of  Vertebrals  is  the  Reptiles,  and  these  are 
either  Chelonians,  Saurians,  Ophidians,  or  Batrachians.  Cuvier 
writes  Batraciem,  but  we  prefer  the  spelling  to  which  the  Greek 
word  directs  us. 

The  next  class  is  the  Fishes,  in  which  province  Cuvier  has 
himself  been  the  great  systematist,  and  has  therefore  had  to  devise 
many  new  terms.  Many  of  these  are  of  Greek  or  Latin  origin, 
and  can  be  anglicized  by  the  analogies  already  pointed  out,  as 
Chondropterygians,  Malacopterygians,  Lophobranchs,  Plectognaths, 
Gymnodonts,  Scleroderms.  Discoboles  and  Apodes  may  be  Eng- 
lish as  well  as  French.  There  are  other  cases  in  which  the 
author  has  formed  the  names  of  families,  either  by  forming  a 
word  in  ides  from  the  name  of  a  genus,  as  Gadoides,  Gobioides, 
or  by  gallicizing  the  Latin  name  of  the  genus,  as  Salmones  from 
Salmo,  Clupes  from  Clupea,  Esoces  from  Esox,  Cyprins  from  Cy- 
prinus.  In  both  these  cases  the  best  procedure  seems  to  be  to 
form  the  English  substantive  in  idan,  as  Gadoidans,  Gobioidans, 
Salmonidans,  Clupeidans,  Esocidans,  Cyprinidans.  One  of  the 
orders  of  fishes,  co-ordinate  with  the  Chondropterygians  and  the 
Lophobranchs,  is  termed  Osseux  by  Cuvier.  It  appears  hardly 
worth  while  to  invent  a  substantive  word  for  this,  when  Bony 
Fishes  is  so  simple  a  phrase,  and  may  readily  be  understood  as  a 
technical  name  of  a  systematic  order. 

The  Mollusks  are  the  next  class  ;  and  these  are  divided  into 
Cephalopods,  Gasteropods,  and  the  like.  The  Gasteropods  are  Nu- 
dibranchs,  Infer obranchs,  Tectibranchs,  Pectinibranchs,  Scuti- 
branchs,  and  Cyclobranchs.  In  framing  most  of  these  terms 
Cuvier  has  made  hybrids  by  a  combination  of  a  Latin  word  with 
branchiae,  which  is  the  Greek  name  for  the  gills  of  a  fish  ;  and 
has  thus  avoided  loading  the  memory  with  words  of  an  origin  not 
obvious  to  most  naturalists,  as  terms  derived  from  the  Greek 


CX11  APHORISMS  CONCERNING 

would  have  been.  Another  division  of  the  Gasteropoda  is  Pul- 
mones,  which  we  must  make  Pulmonians.  In  like  manner  the 
subdivisions  of  the  Pectinibranchs  are  the  Trochoidans  and  BUG- 
einoidans  (Trochdides,  Buccindides).  The  Acephales,  another 
order  of  Mollusks,  may  be  Acephals  in  English. 

After  these  comes  the  third  grand  division  of  Articulated  Ani- 
mals,  and  these  are  Annelidans,  Crustaceans,  Arachnidans,  and 
Insects.  I  shall  not  dwell  upon  the  names  of  these,  as  the  form 
of  English  words  which  is  to  be  selected  must  be  sufficiently 
obvious  from  the  preceding  examples. 

Finally,  we  have  the  fourth  grand  division  of  animals,  the 
llayonnes,  or  Radiata;  which,  for  reasons  already  given,  we  may 
call  Radials.  These  are  Echinoderms,  Intestinals,  Acalephes  and 
Polyps.  The  Polyps,  which  are  composite  animals  in  which  many 
gelatinous  individuals  are  connected  so  as  to  have  a  common  life, 
have,  in  many  cases,  a  more  solid  framework  belonging  to  the  com- 
mon part  of  the  animal.  This  framework,  of  which  coral  is  a 
special  example,  is  termed  in  French  Polypier ;  the  word  has  been 
anglicized  by  the  word  polypary,  after  the  analogy  of  amary  and 
apiary.  Thus  Polyps  are  either  Polyps  with  Polyparies  or  Naked 
Polyps. 

Any  common  kind  of  Polyps  has  usually  in  the  English  lan- 
guage been  called  Polypus,  the  Greek  termination  being  retained. 
This  termination  in  us,  however,  whether  Latin  or  Greek,  is  to 
be  excluded  from  the  English  as  much  as  possible,  on  account  of 
the  embarassment  which  it  occasions  in  the  formation  of  the 
pluraL  For  if  we  say  Polypi  the  word  ceases  to  be  English, 
while  Polypuses  is  harsh :  and  there  is  the  additional  inconveni- 
ence, that  both  these  forms  would  indicate  the  plural  of  individuals 
rather  than  of  classes.  If  we  were  to  say,  "  The  Corallines  are  a 
Family  of  the  Polypuses  with  Polyparies"  it  would  not  at  once 
occur  to  the  reader  that  the  three  last  words  formed  a  technical 
phrase. 

This  termination  us,  which  must  thus  be  excluded  from  the 
names  of  families,  may  be  admitted  in  the  designation  of  genera ; 
of  animals,  as  Nautilus,  Echinus,  Hippopotamus ;  and  of  plants,  as 
Crocus,  Asparagus,  Narcissus,  Acanthus,  Eanunculus,  Fungus. 


THE  LANGUAGE  OF  SCIENCE.  CXiii 

The  same  form  occurs  in  other  technical  words,  as  Fucus,  Mucus, 
(Esophagus,  Hydrocephalus,  Callus,  Calculus,  Uterus,  Foetus, 
Radius,  Focus,  Apparatus.  It  is,  however,  advisable  to  retain 
this  form  only  in  cases  where  it  is  already  firmly  established  in 
the  language ;  for  a  more  genuine  English  form  is  preferable. 
Hence  we  say,  with  Mr.  Lyell,  Icthyosaur,  Plesiosaur,  Ptero- 
dactyl. In  like  manner  Mr.  Owen  anglicizes  the  termination 
erium,  and  speaks  of  the  Anoplothere  and  Paleothere. 

Since  the  wants  of  science  thus  demand  adjectives  which 
can  be  used  also  as  substantive  names  of  classes,  this  consideration 
may  sometimes  serve  to  determine  our  selection  of  new  terms. 
Thus  Mr.  LyelFs  names  for  the  subdivisions  of  the  tertiary  strata, 
Miocene,  Pliocene,  can  be  used  as  substantives ;  but  if  such  words 
as  Mioneous,  Plioneous  had  suggested  themselves,  they  must  have 
been  rejected,  though  of  equivalent  signification,  as  not  fulfilling 
this  condition. 

4.  (1.)  Abstract  substantives  can  easily  be  formed  from  ad- 
jectives :  from  electric  we  h&ve  electricity ;  from  galvanic,  galvan- 
ism ;  from  organic,  organization ;  velocity,  lemty,  gravity,  are 
borrowed  from  Latin  adjectives.  Caloric  is  familiarly  used  for 
the  matter  of  heat,  though  the  form  of  the  word  is  not  supported 
by  any  obvious  analogy. 

(2.)  It  is  quite  intolerable  to  have  words  regularly  formed  in 
opposition  to  the  analogy  which  their  meaning  offers ;  as  when 
bodies  are  said  to  have  conductibiliti/  or  conducibility  with  regard 
to  heat.  The  bodies  are  conduct^  and  their  property  is  con- 
ductivity . 

(3.)  The  terminations  ize  (rather  than  ise),  ism,  and  ist  are 
applied  to  words  of  all  origins :  thus  we  have  to  pulverize,  to 
colonize,  Witticism,  Heathenism,  Journalist,  Tobacconist.  Hence 
we  may  make  such  words  when  they  are  wanted.  As  we  cannot 
use  physician  for  a  cultivator  of  physics,  I  have  called  him  a 
physicist.  We  need  very  much  a  name  to  describe  a  cultivator 
of  science  in  general.  I  should  incline  to  call  him  a  Scientist. 
Thus  we  might  say,  that  as  an  Artist  is  a  Musician,  Painter,  or 
Poet,  a  Scientist  is  a  Mathematician,  Physicist,  or  Naturalist. 

(4.)  Connected  with  verbs  in  ize,  we  have  abstract  nouns  in 


CX1V  APHORISMS   CONCERNING 

ization,  as  polarization,  crystallization,  These  it  appears  proper 
to  spell  in  English  with  z  rather  than  s ;  governing  our  practice 
by  the  Greek  verbal  termination  /£o>  which  we  imitate.  But  we 
must  observe  that  verbs  and  substantives  in  yse,  (analyse,)  belong 
to  a  different  analogy,  giving  an  abstract  noun  in  ysis  and  an 
adjective  ytic  or  ytical ;  (analysis,  analytic,  analytical).  Hence 
electrolyse  is  more  proper  than  electrolyze. 

(5.)  The  names  of  many  sciences  end  in  ics  after  the  analogy 
of  Mathematics,  Metaphysics ;  as  Optics,  Mechanics.  But  these  in 
most  other  languages,  as  in  our  own  formerly,  have  the  singular 
form  Optice,  I'Optique,  Optik,  Optick :  and  though  we  now  write 
Optics,  we  make  such  words  of  the  singular  number :  "  Newton's 
Opticks  is  an  example."  As,  however,  this  connexion  in  new 
words  is  startling,  as  when  we  say,  "  Thermo-electrics  is  now  much 
cultivated,"  it  appears  better  to  employ  the  singular  form,  after 
the  analogy  of  Logic  and  Rhetoric,  when  we  have  words  to  con- 
struct. Hence  we  may  call  the  science  of  languages  Linguistic, 
as  it  is  called  by  the  best  German  writers,  for  instance,  William 
von  Humboldt. 

5.  In  the  derivation  of  English  from  Latin  or  Greek  words, 
the  changes  of  letters  are  to  be  governed  by  the  rules  which  have 
generally  prevailed  in  such  cases.  The  Greek  OL  and  ai,  the 
Latin  oe  and  ae,  are  all  converted  into  a  simple  e,  as  in  Economy, 
Geodesy,  p^nal,  Cesar.  Hence,  according  to  common  usage, 
we  should  write  phenomena,  not  phenomena,  paleontology,  not 
paleontology,  miocene  not  miocome,  pekilite  not  pcekilite.  But 
in  order  to  keep  more  clearly  in  view  the  origin  of  our  terms,  it 
may  be  allowable  to  deviate  from  these  rules  of  change,  especially 
so  long  as  the  words  are  still  new  and  unfamiliar.  Dr.  Buckland 
speaks  of  the  poikilitic,  not  pecilitic,  group  of  strata :  palaeontology 
is  the  spelling  commonly  adopted;  and  in  imitation  of  this  I 
have  VfiiitQTipalwtiology.  The  diphthong  et  was  by  the  Latins 
changed  into  i,  as  in  Arist^des;  and  hence  this  has  been  the 
usual  form  in  English.  Some  recent  authors  indeed  (Mr.  Mitford 
for  instance)  write  Ariste^des ;  but  the  former  appears  to  be  the 
more  legitimate.  Hence  we  write  nuocene,  pKocene,  not  meio- 
cene,  pliocene.  The  Greek  t>  becomes  y,  and  ov  becomes  u,  in 


THE    LANGUAGE    OF    SCIENCE.  CXV 

English  as  in  Latin,  as  crystal,  colure.  The  consonants  K  and  % 
become  c  and  ch  according  to  common  usage.  Hence  we  write 
crystal,  not  chrystal,  batrac/jian  not  batracian,  cryolite,  not  Cryo- 
lite. As,  however,  the  letter  c  before  £  and  i  differs  from  k,  which 
is  the  sound  we  assign  to  the  Greek  K,  it  may  be  allowable  to  use 
k  in  order  to  avoid  this  confusion.  Thus,  as  we  have  seen,  poi&ilite 
has  been  used,  as  well  as  pecilite.  Even  in  common  language 
some  authors  write  sceptic,  which  appears  to  be  better  than  scep- 
tic with  our  pronunciation,  and  is  preferred  by  Dr.  Johnson. 
For  the  same  reason,  namely  to  avoid  confusion  in  the  pronuncia- 
tion, and  also,  in  order  to  keep  in  view  the  connexion  with 
cathode,  the  elements  of  an  electrolyte  which  go  to  the  anode  and 
cathode  respectively  may  be  termed  the  anion  and  catfaon ; 
although  the  Greek  would  suggest  cation,  (/car iov). 

6.  The  example  of  chemistry  has  shown  that  we  have  in  the 
terminations  of  words  a  resource  of  which  great  use  may  be  made 
in  indicating  the  relations  of  certain  classes  of  objects :  as  sul- 
-phurous  and  sulphur/0  acids ;  sulphates,  sulphites,  and  sulphurets. 
Since  the  introduction  of  the  artifice  by  the  Lavoisierian  school,  it 
has  been  extended  to  some  new  cases.     Thus  Chlorm^,  Fluorine, 
Bromine,  Iodine,  had  their  names  put  into  that  shape  in  conse- 
quence of  their  supposed  analogy :    and  for  the  same  reason  have 
been  termed  Chlore,  Phtore,  Brome,  lode,  by  French  chemists. 
In  like  manner,  the  names  of  metals  in  their  Latin  form  have 
been  made  to  end  in  um,  as  Osmium,  Palladium  ;  and  hence  it  is 
better  to  say  Platimm,  Molybdenum,  than  Plating,  Molybdena. 
It  has  been  proposed  to  term  the  basis  of  Boracic  acid  Boron; 
and  those  who  conceive  that  the  basis  of  Silica  has  an  analogy 
with  Boron  have  proposed  to  term  it  Silicon,  while  those  who 
look  upon  it  as  a  metal  would  name  it  Silicium.      Selenium  was 
so  named  when  it  was  supposed  to  be  a  metal :    as  its  analogies 
are  now  acknowledged  to  be  of  another  kind,  it  would  be  desirable, 
if  the  change  were  not  too  startling,  to  term  it  Selen,  as  it  is  in 
German.     Phospho/w  in  like  manner  might  be  Phosphor,  which 
would  indicate  its  analogy  with  Sulphur. 

The  resource  which  terminations  offer  has  been  applied  in 
other  cases.     The  names  of  many  species  of  minerals  end  in  lite, 


CXV1  APHORISMS    CONCERNING 

or  ite,  as  Stauro&'te,  Augite.  Hence  Adolphe  Brongniart,  in  .order 
to  form  a  name  for  a  genus  of  fossil  plants,  has  given  this  termi- 
nation to  the  name  of  the  recent  genus  which  they  nearly  resem- 
ble, as  Zaanites  from  Zamia,  Lycopodto  from  Lycopodium. 

Names  of  different  genera  which  differ  in  termination  only 
are  properly  condemned  by  Linnaeus*;  as  Alsine,  Alsinoides, 
Alsinella,  Alsinastrum ;  for  there  is  no  definite  relation  marked 
by  those  terminations.  Linnaeus  gives  to  such  genera  distinct 
names,  Alsine,  Bufonia,  Sagina,  Elatine. 

Terminations  are  well  adapted  to  express  definite  systematic 
relations,  such  as  those  of  chemistry,  but  they  must  be  employed 
with  a  due  regard  to  all  the  bearings  of  the  system.  Davy 
proposed  to  denote  the  combinations  of  other  substances  with 
chlorine  by  peculiar  terminations ;  using  ane  for  the  smallest 
proportion  of  Chlorine,  and  anea  for  the  larger,  as  Cuprane, 
Cupranea.  In  this  nomenclature,  common  salt  would  be  Sodane, 
and  Chloride  of  Nitrogen  would  be  Azotane.  This  suggestion 
never  found  favour.  It  was  objected  that  it  was  contrary  to  the 
Linnsean  precept,  that  a  specific  name  must  not  be  united  to  a 
generic  as  a  termination.  But  this  was  not  putting  the  matter 
exactly  on  its  right  ground ;  for  the  rules  of  nomenclature  of 
natural  history  do  not  apply  to  chemistry ;  and  the  Linnsean  rule 
might  with  equal  propriety  have  been  adduced  as  a  condemnation 
of  such  terms  as  Sulphurous,  Sulphur^.  But  Davy's  terms  were 
bad ;  for  it  does  not  appear  that  Chlorine  enters,  as  Oxygen  does, 
into  so  large  a  portion  of  chemical  compounds,  that  its  relations 
afford  a  key  to  their  nature,  and  may  properly  be  made  an 
element  in  their  names. 

This  resource,  of  terminations,  has  been  abused,  wherever  it 
has  been  used  wantonly,  or  without  a  definite  significance  in  the 
variety.  This  is  the  case  in  M.  Beudanfs  Mineralogy.  Among 
the  names  which  he  has  given  to  new  species,  we  find  the  follow- 
ing (besides  many  in  ite),  Scolexero^,  Opsimose,  Exanthelo^, 
&c.;  Diacras^,  Panabas^,  Neopk&?;  Neocl^,-  Rhode/*?,  Stibi- 
comX  &c. ;  Marcel^,  Wilhelnuw*,  Sec.;  Exited,  and  many 
others.  In  addition  to  other  objections  which  might  be  made 
*  Phil.  J3ot.,  231. 


THE  LANGUAGE  OF  SCIENCE.  CXV11 

to  these  names,  their  variety  is  a  material  defect :  for  to  make 
this  variety  depend  on  caprice  alone,  as  in  those  cases  it  does,  is 
to  throw  away  a  resource  of  which  chemical  nomenclature  may 
teach  us  the  value. 

APHORISM  XVII. 

When  alterations  in  technical  terms  become  necessary,  it  is  desirable 
that  the  new  term  should  contain  in  its  form  some  memorial  of 
the  old  one. 

WE  have  excellent  examples  of  the  advantageous  use  of  this 
maxim  in  Linnseus^s  reform  of  botanical  nomenclature.  His 
innovations  were  very  extensive,  but  they  were  still  moderated  as 
much  as  possible,  and  connected  in  many  ways  with  the  names 
of  plants  then  in  use.  He  has  himself  given  several  rules  of 
nomenclature,  which  tend  to  establish  this  connexion  of  the 
old  and  new  in  a  reform.  Thus  he  says,  "  Generic  names 
which  are  current,  and  are  not  accompanied  with  harm  to  botany, 
should  be  tolerated*."  "A  passable  generic  name  is  not  to  be 
changed  for  another,  though  more  apt-)-."  New  generic  names 
are  not  to  be  framed  so  long  as  passable  synonyms  are  at  hand!." 
"  A  generic  name  of  one  genus,  except  it  be  superfluous,  is  not 
to  be  transferred  to  another  genus,  though  it  suit  the  other 
better  §."  "  If  a  received  genus  requires  to  be  divided  into 
several,  the  name  which  before  included  the  whole,  shall  be 
applied  to  the  most  common  and  familiar  kind  1 1."  And  though 
he  rejects  all  generic  names  which  have  not  a  Greek  or  Latin 
rootU,  he  is  willing  to  make  an  exception  in  favour  of  those 
which  from  their  form  might  be  supposed  to  have  such  a  root, 
though  they  are  really  borrowed  from  other  languages,  as  Theay 
which  is  the  Greek  for  goddess  ;  Coffea,  which  might  seem  to  come 
from  a  Greek  word  denoting  silence  (/e&>0o<?) ;  Cheiranthus, 
which  appears  to  mean  hand-flower,  but  is  really  derived  from 
the  Arabic  Keiri  :  and  many  others. 

As  we  have  already  said,  the  attempt  at  a  reformation  of  the 

*  Philosophia  Botanica,  Art.  242.  t  P.  246.  J  P.  247. 

§  P.  249.  |j  P.  249.  1T  P.  232. 


CXviii  APHORISMS  CONCERNING 

nomenclature  of  Mineralogy  made  by  Professor  Mohs  will  pro- 
bably not  produce  any  permanent  effect,  on  this  account  amongst 
others,  that  it  has  not  been  conducted  in  this  temperate  mode  ; 
the  innovations  bear  too  large  a  proportion  to  the  whole  of  the 
names,  and  contain  too  little  to  remind  us  of  the  known  appella- 
tions. Yet  in  some  respects  Professor  Mohs  has  acted  upon  this 
maxim.  Thus  he  has  called  one  of  his  classes  Spar,  because 
Felspar  belongs  to  it.  I  shall  venture  to  offer  a  few  suggestions 
on  this  subject  of  mineralogical  nomenclature. 

It  has  already  been  remarked  that  the  confusion  and  complexity 
which  prevail  in  this  subject  render  a  reform  very  desirable. 
But  it  will  be  seen,  from  the  reasons  assigned  under  the  Ninth 
Aphorism,  that  no  permanent  system  of  names  can  be  looked  for, 
till  a  sound  system  of  classification  be  established.  The  best 
mineralogical  systems  recently  published,  however,  appear  to  con- 
verge to  a  common  point ;  and  certain  classes  have  been  formed 
which  have  both  a  natural-historical  and  a  chemical  significance. 
These  Classes,  according  to  Naumann,  whose  arrangement  appears 
the  best,  are  Hydrolytes,  Haloids,  Silicides,  Oxides  of  Metals, 
Metals,  Sulphurides  (Pyrites,  Glances,  and  Blendes),  and  Anthra- 
cides.  Now  we  find ; — that  the  Hydrolytes  are  all  compounds, 
such  as  are  commonly  termed  Salts ; — that  the  Haloids  are,  many 
of  them,  already  called  Spars,  as  Calc  Spar,  Heavy  Spar,  Iron 
Spar,  Zinc  Spar ; — that  the  Silicides,  the  most  numerous  and 
difficult  class,  are  denoted  for  the  most  part,  by  single  words, 
many  of  which  end  in  ite ; — that  the  other  classes,  or  sub-classes, 
Oxides,  Pyrites,  Glances,  and  Blendes,  have  commonly  been  so 
termed ;  as  Red  Iron  Oxide,  Iron  Pyrites,  Zinc  Blende  ; — while 
pure  metals  have  usually  had  the  adjective  Native  prefixed, 
as  Native  Gold,  Native  Copper.  These  obvious  features  of 
the  current  names  appear  to  afford  us  a  basis  for  a  systematic 
nomenclature.  The  Salts  and  Spars  might  all  have  the  word 
salt  or  spar  included  in  their  name,  as  Natron  Salt,  Glauber 
Salt,  Hock  Salt ;  Calc  Spar,  Bitter  Spar  (Carbonate  of  Lime 
and  Magnesia),  Fluor  Spar,  Phosphor  Spar  (Phosphate  of 
Lime),  Heavy  Spar,  Celestine  Spar  (Sulphate  of  Strontian), 
Chromic  Lead  Spar  (Chromate  of  Lead)  ;  the  Silicides  might  all 


THE  LANGUAGE  OF  SCIENCE. 

have  the  name  constructed  so  as  to  be  a  single  word  ending  in  ite, 
as  Chabasite  (Chabasie),  Natr elite  (Mesotype),  Sommite  (Nephe- 
line),  Pistacite  (Epidote)  ;  from  this  rule  might  be  excepted  the 
Gems,  as  Topaz,  Emerald,  Corundum,  which  might  retain  their 
old  names.  The  Oxides,  Pyrites,  Glances,  and  Blendes,  might  be 
so  termed ;  thus  we  should  have  Tungstic  Iron  Oxide  (usually 
called  Tungstate  of  Iron),  Arsenical  Iron  Pyrites  (Mispickel), 
Tetrahedral  Copper  Glance  (Fahlerz),  Quicksilver  Blende  (Cinna- 
bar), and  the  Metals  might  be  termed  native,  as  Native  Copper, 
Native  Silver. 

Such  a  nomenclature  would  take  in  a  very  large  proportion  of 
commonly  received  appellations,  especially  if  we  were  to  select 
among  the  synonyms,  as  is  proposed  above  in  the  case  of  Glauber 
Salt,  Bitter  Spar,  Sommite,  Pistacite,  Natrolite.  Hence  it  might 
be  adopted  without  serious  inconvenience.  It  would  make  the 
name  convey  information  respecting  the  place  of  the  mineral  in 
the  system;  and  by  imposing  this  condition,  would  limit  the 
extreme  caprice,  both  as  to  origin  and  form,  which  has  hitherto 
been  indulged  in  imposing  mineralogical  names. 

The  principle  of  a  mineralogical  nomenclature  determined  by 
the  place  of  the  species  in  the  system,  has  been  recognized  by  Mr. 
Beudant  as  well  as  Mr.  Mohs.  The  former  writer  has  proposed 
that  we  should  say  Carbonate  Calcaire,  Carbonate  Witherite,  Sul- 
phate Couperose,  Silicate  Stilbite,  Silicate  Chabasie,  and  so  on. 
But  these  are  names  in  which  the  part  added  for  the  sake  of  the 
system  is  not  incorporated  with  the  common  name,  and  would 
hardly  make  its  way  into  common  use. 

We  have  already  noticed  Mr.  Mohs's  designations  for  two  of 
the  Systems  of  Crystallization,  the  Pyramidal  and  the  Pris- 
matic, as  not  characteristic.  If  it  were  thought  advisable  to  re- 
form such  a  defect,  this  might  be  done  by  calling  them  the 
Square  Pyramidal  and  the  Oblong  Prismatic,  which  terms,  while 
they  expressed  the  real  distinction  of  the  systems,  would  be  intel- 
ligible at  once  to  those  acquainted  with  the  Mohsian  terminology. 

I  will  mention  another  suggestion  respecting  the  introduction  of 
an  improvement  in  scientific  language.  The  term  Depolarization 
was  introduced,  because  it  was  believed  that  the  effect  of  certain 


CXX      APHORISMS  CONCERNING  THE  LANGUAGE  OF  SCIENCE. 

crystals,  when  polarized  light  was  incident  upon  them  in  certain 
positions,  was  to  destroy  the  peculiarity  which  polarization  had 
produced.  But  it  is  now  well  known  that  the  effect  of  the  second 
crystal  in  general  is  to  divide  the  polarized  ray  of  light  into  two 
rays,  polarized  in  different  planes.  Still  this  effect  is  often  spoken 
of  as  Depolarization,  no  better  term  having  been  yet  devised.  I 
have  proposed  and  used  the  term  Depolarization,  which  well  ex- 
presses what  takes  place,  and  so  nearly  resembles  the  older  word, 
that  it  must  sound  familiar  to  those  already  acquainted  with 
writings  on  this  subject. 

I  may  mention  one  term  in  another  department  of  literature 
which  it  appears  desirable  to  reform  in  the  same  manner.  The 
theory  of  the  Fine  Arts,  or  the  philosophy  which  speculates  con- 
cerning what  is  beautiful  in  painting,  sculpture  or  architecture, 
and  other  arts,  often  requires  to  be  spoken  of  in  a  single  word. 
Baumgarten  and  other  German  writers  have  termed  this  province 
of  speculation  ^Esthetics ;  aicrddvecrOai,  to  perceive,  being  a  word 
which  appeared  to  them  fit  to  designate  the  perception  of  beauty 
in  particular.  Since,  however,  aesthetics  would  naturally  denote 
the  doctrine  of  perception  ;  since  this  doctrine  requires  a  name  ; 
since  the  term  aesthetics  has  actually  been  applied  to  it  by  other 
German  writers  (as  Kant)  ;  and  since  the  essential  point  in  the 
philosophy  now  spoken  of  is  that  it  attends  to  beauty; — it  appears 
desirable  to  change  this  name.  In  pursuance  of  the  maxim  now 
before  us,  I  should  propose  the  term  Callwsthetics,  or  rather  (in 
agreement  with  what  was  said  in  page  cxiv.)  Callwsthetic,  the 
science  of  the  perception  of  beauty. 

I  may  here  notice  a  principle  which  may  sometimes  be  allowed 
to  influence  us,  in  selecting  one  form  rather  than  another  for  a 
technical  term.  It  is  convenient  to  make  correlative  terms  re- 
semble each  other  in  termination,  even  when  the  resemblance  is 
only  apparent ;  thus  we  may  speak  of  marine  and  terrene  animals, 
rather  than  terrestrial  or  tellurian.  Dr.  Prichard  speaks  of  car- 
nivorous wAphytiborous  insects ;  preferring  the  latter  term  to  phy- 
tophagous, on  account  of  its  sound,  I  suppose,  as  well  as  for  other 
reasons. 


THE 

• 

PHILOSOPHY 


OF   THE 


INDUCTIVE    SCIENCES. 


PART  I. 

OF  IDEAS. 


VOL.  I.  B 


adhuc  inventa  sunt  in  Scientiis,  ea  hujusmodi  simt 
ut  notionibus  vulgaribus  fere  subjaceant :  ut  vero  ad 
interiora  et  remotiora  naturas  penetretur,  necesse  est  ut 
tarn  NOTIONES  quam  AXIOMATA  magis  certa  et  munita 
via  a  particularibus  abstrahantur ;  atque  omnino  melior 
et  certior  intellectus  adoperatio  in  ustim  veniat. 

BACON,  Nov.  Org.,  Lib.  1.  Aphor.  xviii. 


BOOK   I. 


OF  IDEAS    IN    GENERAL. 


CHAPTER  I. 
INTRODUCTION. 

THE  PHILOSOPHY  OF  SCIENCE,  if  the  phrase  were  to  be 
understood  in  the  comprehensive  sense  which  most  natu- 
rally offers  itself  to  our  thoughts,  would  imply  nothing 
less  than  a  complete  insight  into  the  essence  and  con- 
ditions of  all  real  knowledge,  and  an  exposition  of  the 
best  methods  for  the  discovery  of  new  truths.  We  must 
narrow  and  lower  this  conception,  in  order  to  mould  it 
into  a  form  in  which  we  may  make  it  the  immediate 
object  of  our  labours  with  a  good  hope  of  success ;  yet 
still  it  may  be  a  rational  and  useful  undertaking,  to 
endeavour  to  make  some  advance  towards  such  a  Philo- 
sophy, even  according  to  the  most  ample  conception  of  it 
which  we  can  form.  The  present  work  has  been  written 
with  a  view  of  contributing,  in  some  measure,  however 
small  it  may  be,  towards  such  an  undertaking. 

But  in  this,  as  in  every  attempt  to  advance  beyond 
the  position  which  we  at  present  occupy,  our  hope  of 
success  must  depend  mainly  upon  our  being  able  to  profit, 
to  the  fullest  extent,  by  the  progress  already  made.  We 
may  best  hope  to  understand  the  nature  and  conditions 
of  real  knowledge,  by  studying  the  nature  and  conditions 
of  the  most  certain  and  stable  portions  of  knowledge 
which  we  already  possess :  and  we  are  most  likely  to 
learn  the  best  methods  of  discovering  truth,  by  examin- 

B  2 


4:  OF   IDEAS    IN   GENERAL. 

ing  how  truths,  now  universally  recognised,  have  really 
been  discovered.  Now  there  do  exist  among  us  doc- 
trines of  solid  and  acknowledged  certainty,  and  truths  of 
which  the  discovery  has  been  received  with  universal 
applause.  These  constitute  what  we  commonly  term 
Sciences;  and  of  these  bodies  of  exact  and  enduring 
knowledge,  we  have  within  our  reach  so  large  and  varied 
a  collection,  that  we  may  examine  them,  and  the  history 
of  their  formation,  with  a  good  prospect  of  deriving  from 
the  study  such  instruction  as  we  seek.  We  may  best 
hope  to  make  some  progress  towards  the  Philosophy  of 
Science,  by  employing  ourselves  upon  THE  PHILOSOPHY 
OF  THE  SCIENCES. 

The  sciences  to  which  the  name  is  most  commonly 
and  unhesitatingly  given,  are  those  which  are  concerned 
about  the  material  world;  whether  they  deal  with  the 
celestial  bodies,  as  the  sun  and  stars,  or  the  earth  and  its 
products,  or  the  elements ;  whether  they  consider  the 
differences  which  prevail  among  such  objects,  or  their 
origin,  or  their  mutual  operation.  And  in  all  these 
sciences  it  is  familiarly  understood  and  assumed,  that 
their  doctrines  are  obtained  by  a  common  process  of  col- 
lecting general  truths  from  particular  observed  facts, 
which  process  is  termed  Induction.  It  is  further  assumed 
that  both  in  these  and  in  other  provinces  of  knowledge, 
so  long  as  this  process  is  duly  and  legitimately  performed? 
the  results  will  be  real  substantial  truth.  And  although 
this  process,  with  the  conditions  under  which  it  is 
legitimate,  and  the  general  laws  of  the  formation  of 
sciences,  will  hereafter  be  subjects  of  discussion  in  this 
work,  I  shall  at  present  so  far  adopt  the  assumption  of 
which  I  speak,  as  to  give  to  the  sciences  from  which  our 
lessons  are  to  be  collected  the  name  of  Inductive  sciences. 
And  thus  it  is  that  I  am  led  to  designate  my  work  as 
THE  PHILOSOPHY  OF  THE  INDUCTIVE  SCIENCES. 


INTRODUCTION.  5 

The  views  respecting  the  nature  and  progress  of 
knowledge,  towards  which  we  shall  be  directed  by  such  a 
course  of  inquiry  as  I  have  pointed  out,  though  derived 
from  those  portions  of  human  knowledge  which  are  more 
peculiarly  and  technically  termed  Sciences,  will  by  no 
means  be  confined,  in  their  bearing,  to  the  domain  of  such 
sciences  as  deal  with  the  material  world,  nor  even  to  the 
whole  range  of  sciences  now  existing.  On  the  contrary, 
we  shall  be  led  to  believe  that  the  nature  of  truth  is  in  all 
subjects  the  same,  and  that  its  discovery  involves,  in  all 
cases,  the  like  conditions.  On  one  subject  of  human 
speculation  after  another,  man's  knowledge  assumes  that 
exact  and  substantial  character  which  leads  us  to  term  it 
Science ;  and  in  all  these  cases,  whether  inert  matter  or 
living  bodies,  whether  permanent  relations  or  successive 
occurrences  be  the  subject  of  our  attention,  we  can  point 
out  certain  universal  characters  which  belong  to  truth, 
certain  general  laws  which  have  regulated  its  progress 
among  men.  And  we  naturally  expect  that  even  when  we 
extend  our  range  of  speculation  wider  still,  when  we 
contemplate  the  world  within  us  as  well  as  the  world 
without  us,  when  we  consider  the  thoughts  and  actions  of 
men  as  well  as  the  motions  and  operations  of  unintelli- 
gent bodies,  we  shall  still  find  some  general  analogies 
which  belong  to  the  essence  of  truth,  and  run  through 
the  whole  intellectual  universe.  Hence  we  have  reason 
to  trust  that  a  just  philosophy  of  the  sciences  may  throw 
light  upon  the  nature  and  extent  of  our  knowledge  in 
every  department  of  human  speculation.  By  considering 
what  is  the  real  import  of  our  acquisitions,  where  they  are 
certain  and  definite,  we  may  learn  something  respecting 
the  difference  between  true  knowledge  and  its  precarious 
or  illusory  semblances ;  by  examining  the  steps  by  which 
such  acquisitions  have  been  made,  we  may  discover  the 
conditions  under  which  truth  is  to  be  obtained ;  by 


6  OF    IDEAS    IN    GENERAL. 

tracing  the  boundary-line  between  our  knowledge  and 
our  ignorance,  we  may  ascertain  in  some  measure  the 
extent  of  the  powers  of  man's  understanding. 

But  it  may  be  said,  in  such  a  design  there  is  nothing 
new ;  these  are  objects  at  which  inquiring  men  have  often 
before  aimed.  To  determine  the  difference  between  real 
and  imaginary  knowledge,  the  conditions  under  which  wre 
arrive  at  truth,  the  range  of  the  powers  of  the  human 
mind,  has  been  a  favourite  employment  of  speculative 
men  from  the  earliest  to  the  most  recent  times.  To 
inquire  into  the  original,  certainty,  and  compass  of  man's 
knowledge,  the  limits  of  his  capacity,  the  strength  and 
weakness  of  his  reason,  has  been  the  professed  purpose  of 
many  of  the  most  conspicuous  and  valued  labours  of  the 
philosophers  of  all  periods  up  to  our  own  day.  It  may 
appear,  therefore,  that  there  is  little  necessity  to  add  one 
more  to  these  numerous  essays ;  and  little  hope  that  any 
new  attempt  will  make  any  very  important  addition  to 
the  stores  of  thought  upon  such  questions,  which  have 
been  accumulated  by  the  profoundest  and  acutest  thinkers 
of  all  ages. 

To  this  I  reply,  that  without  at  all  disparaging  the 
value  or  importance  of  the  labours  of  those  who  have 
previously  written  respecting  the  foundations  and  con- 
ditions of  human  knowledge,  it  may  still  be  possible  to 
add  something  to  what  they  have  clone.  The  writings  of 
all  great  philosophers,  up  to  our  own  time,  form  a  series 
which  is  not  yet  terminated.  The  books  and  systems  of 
philosophy  which  have,  each  in  its  own  time,  won  the  ad- 
miration of  men,  and  exercised  a  powerful  influence  upon 
their  thoughts,  have  had  each  its  own  part  and  functions 
in  the  intellectual  history  of  the  world ;  and  other 
labours  wrhich  shall  succeed  these  may  also  have  their 
proper  office  and  useful  effect.  We  may  not  be  able  to 
do  much,  and  yet  still  it  may  be  in  our  power  to  effect 


INTRODUCTION.  7 

something.  Perhaps  the  very  advances  made  by  former 
inquirers  may  have  made  it  possible  for  us,  at  present,  to 
advance  still  further.  In  the  discovery  of  truth,  in  the 
developement  of  man's  mental  powers  and  privileges, 
each  generation  has  its  assigned  part;  and  it  is  for  us  to 
endeavour  to  perform  our  portion  of  this  perpetual  task 
of  our  species.  Although  the  terms  which  describe  our 
undertaking  may  be  the  same  which  have  often  been  em- 
ployed by  previous  writers  to  express  their  purpose,  yet 
our  position  is  different  from  theirs,  and  thus  the  result 
may  be  different  too.  We  have,  as  they  had,  to  run  our 
appropriate  course  of  speculation  with  the  exertion  of 
our  best  powers ;  but  our  course  lies  in  a  more  advanced 
part  of  the  great  line  along  wiiich  philosophy  travels 
from  age  to  age.  However  familiar  and  old,  therefore, 
be  the  design  of  such  a  work  as  this,  the  execution 
may  have,  and  if  it  be  performed  in  a  manner  suitable 
to  the  time,  will  have,  something  that  is  new  and  not 
unimportant. 

Indeed,  it  appears  to  be  absolutely  necessary,  in  order 
to  check  the  prevalence  of  grave  and  pernicious  error, 
that  the  doctrines  which  are  taught  concerning  the  foun- 
dations of  human  knowledge  and  the  powers  -of  the 
human  mind,  should  be  from  time  to  time  revised  and 
corrected  or  extended.  Erroneous  and  partial  views  are 
promulgated  and  accepted ;  one  portion  of  the  truth  is 
insisted  upon  to  the  undue  exclusion  of  another;  or 
principles  true  in  themselves  are  exaggerated  till  they 
produce  on  men's  minds  the  effect  of  falsehood.  When 
evils  of  this  kind  have  grown  to  a  serious  height,  a  reform- 
is  requisite.  The  faults  of  the  existing  systems  must  be 
remedied  by  correcting  what  is  wrong,  and  supplying 
what  is  wanting.  In  such  cases,  all  the  merits  and  ex- 
cellencies of  the  labours  of  the  preceding  times  do  not 
supersede  the  necessity  of  putting  forth  new  views  suited 


8  OF   IDEAS   IN    GENERAL. 

to  the  emergency  which  has  arrived.  The  new  form 
which  error  has  assumed  makes  it  proper  to  endeavour  to 
give  a  new  and  corresponding  form  to  truth.  Thus  the 
mere  progress  of  time,  and  the  natural  growth  of  opinion 
from  one  stage  to  another,  leads  to  the  production  of 
new  systems  and  forms  of  philosophy.  It  will  be  found, 
I  think,  that  some  of  the  doctrines  now  most  widely  pre- 
valent respecting  the  foundations  and  nature  of  truth  are 
of  such  a  kind  that  a  reform  is  needed.  The  present  age 
seems,  by  many  indications,  to  be  called  upon  to  seek  a 
sounder  philosophy  of  knowledge  than  is  now  current 
among  us.  To  contribute  towards  such  a  philosophy  is 
the  object  of  the  present  work.  The  work  is,  therefore, 
like  all  works  which  take  into  account  the  most  recent 
forms  of  speculative  doctrine,  invested  with  a  certain 
degree  of  novelty  in  its  aspect  and  import,  by  the  mere 
time  and  circumstances  of  its  appearance. 

But,  moreover,  we  can  point  out  a  very  important 
peculiarity  by  which  this  work  is,  in  its  design,  distin- 
guished from  preceding  essays  on  like  subjects ;  and  this 
difference  appears  to  be  of  such  a  kind  as  may  well  en- 
title us  to  expect  some  substantial  addition  to  our  know- 
ledge as  the  result  of  our  labours.  The  peculiarity  of 
which  I  speak  has  already  been  announced ; — it  is  this : 
that  we  purpose  to  collect  our  doctrines  concerning  the 
nature  of  knowledge,  and  the  best  mode  of  acquiring  it, 
from  a  contemplation  of  the  structure  and  history  of 
those  sciences  (the  material  sciences),  which  are  univer- 
sally recognised  as  the  clearest  and  surest  examples  of 
knowledge  and  of  discovery.  It  is  by  surveying  and 
studying  the  whole  mass  of  such  sciences,  and  the  vari- 
ous steps  of  their  progress,  that  we  now  hope  to  approach 
to  the  true  Philosophy  of  Science. 

Now  this,  I  venture  to  say,  is  a  new  method  of  pur- 
suing the  philosophy  of  human  knowledge.  Those  who 


INTRODUCTION.  9 

have  hitherto  endeavoured  to  explain  the  nature  of  know- 
ledge, and  the  process  of  discovery,  have,  it  is  true,  often 
illustrated  their  views  by  adducing  special  examples  of 
truths  which  they  conceived  to  be  established,  and  by 
referring  to  the  mode  of  their  establishment.  But  these 
examples  have,  for  the  most  part,  been  taken  at  random, 
not  selected  according  to  any  principle  or  system.  Often 
they  have  involved  doctrines  so  precarious  or  so  vague 
that  they  confused  rather  than  elucidated  the  subject  J 
and  instead  of  a  single  difficulty, — What  is  the  nature 
of  knowledge?  these  attempts  at  illustration  introduced 
two, — What  was  the  true  analysis  of  the  doctrines  thus 
adduced?  and, — Whether  they  might  safely  be  taken  as 
types  of  real  knowledge  ? 

This  has  usually  been  the  case  when  there  have  been 
adduced,  as  standard  examples  of  the  formation  of  human 
knowledge,  doctrines  belonging  to  supposed  sciences  other 
than  the  material  sciences ; — doctrines,  for  example, 
of  political  economy,  or  philology,  or  morals,  or  the  phi- 
losophy of  the  fine  arts.  I  am  very  far  from  thinking 
that,  in  regard  to  such  subjects,  there  are  no  important 
truths  hitherto  established :  but  it  would  seem  that  those 
truths  which  have  been  obtained  in  these  provinces  of 
knowledge,  have  not  yet  been  fixed  by  means  of 
distinct  and  permanent  phraseology,  and  sanctioned 
by  universal  reception,  and  formed  into  a  connected 
system,  and  traced  through  the  steps  of  their  gradual 
discovery  and  establishment,  so  as  to  make  them  in- 
structive examples  of  the  nature  and  progress  of  truth 
in  general.  Hereafter  we  trust  to  be  able  to  show  that 
the  progress  of  moral,  and  political,  and  philological,  and 
other  knowledge,  is  governed  by  the  same  laws  as  that 
of  physical  science.  But  since,  at  present,  the  former 
class  of  subjects  are  full  of  controversy,  doubt,  and 
obscurity,  while  the  latter  consist  of  undisputed  truths 


10  OF   IDEAS    IN    GENERAL. 

clearly  understood  and  expressed,  it  may  be  considered 
a  wise  procedure  to  make  the  latter  class  of  doctrines 
the  basis  of  our  speculations.  And  on  the  having  taken 
this  course,  is,  in  a  great  measure,  my  hope  founded,  of 
obtaining  valuable  truths  which  have  escaped  preceding 
inquirers. 

But  it  may  be  said  that  many  preceding  writers  on 
the  nature  and  progress  of  knowledge  have  taken  their 
examples  abundantly  from  the  physical  sciences.  It 
would  be  easy  to  point  out  admirable  works,  which  have 
appeared  during  the  present  and  former  generations,  in 
which  instances  of  discovery,  borrowed  from  the  physical 
sciences,  are  introduced  in  a  manner  most  happily 
instructive.  And  to  the  works  in  which  this  has  been 
done,  I  gladly  give  my  most  cordial  admiration.  But  at 
the  same  time  I  may  venture  to  remark  that  there  still 
remains  a  difference  between  my  design  and  theirs :  and 
that  I  use  the  physical  sciences  as  exemplifications  of  the 
general  progress  of  knowledge  in  a  manner  very  mate- 
rially different  from  the  course  which  is  followed  in  works 
such  as  are  now  referred  to.  For  the  conclusions  stated 
in  the  present  work,  respecting  knowledge  and  discovery, 
are  drawn  from  a  connected  and  systematic  survey  of  the 
whole  range  of  physical  science  and  its  history;  whereas, 
hitherto,  philosophers  have  contented  themselves  with 
adducing  detached  examples  of  scientific  doctrines,  drawn 
from  one  or  two  departments  of  science.  So  long  as  we 
select  our  examples  in  this  arbitrary  and  limited  manner 
we  lose  the  best  part  of  that  philosophical  instruction, 
which  the  sciences  are  fitted  to  afford  when  we  consider 
them  as  all  members  of  one  series,  and  as  governed  by  rules 
which  are  the  same  for  all.  Mathematical  and  chemical 
truths,  physical  and  physiological  doctrines,  the  sciences  of 
classification  and  of  causation,  must  alike  be  taken  into 
our  account,  in  order  that  we  may  learn  what  are  the 


INTRODUCTION.  11 

general  characters  of  real  knowledge.  When  our  con- 
clusions assume  so  comprehensive  a  shape  that  they  apply 
to  a  range  of  subjects  so  vast  and  varied  as  these,  we 
may  feel  some  confidence  that  they  represent  the  genuine 
form  of  universal  and  permanent  truth.  But  if  our 
exemplification  is  of  a  narrower  kind,  it  may  easily 
cramp  and  disturb  our  philosophy.  We  may,  for  instance, 
render  our  views  of  truth  and  its  evidence  so  rigid  and 
confined  as  to  be  quite  worthless,  by  founding  them  too 
much  on  the  contemplation  of  mathematical  truth.  We 
may  overlook  some  of  the  most  important  steps  in  the 
general  course  of  discovery,  by  fixing  our  attention  too 
exclusively  upon  some  one  conspicuous  group  of  dis- 
coveries, as,  for  instance,  those  of  Newton.  We  may 
misunderstand  the  nature  of  physiological  discoveries,  by 
attempting  to  force  an  analogy  between  them  and  dis- 
coveries of  mechanical  laws,  without  attending  to  the 
intermediate  sciences  which  fill  up  the  vast  interval 
between  these  extreme  terms  in  the  series  of  material 
sciences.  In  these  and  in  many  other  ways,  a  partial 
and  arbitrary  reference  to  the  material  sciences  in  our 
inquiry  into  human  knowledge  may  mislead  us ;  or  at 
least  may  fail  to  give  us  those  wider  views,  and  that 
deeper  insight,  which  should  result  from  a  systematic  study 
of  the  whole  range  of  sciences  with  this  particular  object. 

The  design  of  the  following  work,  then,  is  to  form  a 
Philosophy  of  Science,  by  analysing  the  substance  and 
examining  the  progress  of  the  existing  body  of  the 
sciences.  As  a  preliminary  to  this  undertaking,  a  survey 
of  the  history  of  the  sciences  was  necessary.  This, 
accordingly,  I  have  already  performed ;  and  the  result  of 
the  labour  thus  undertaken  has  been  laid  before  the 
public  as  a  History  of  the  Inductive  Sciences. 

In  that  work  I  have  endeavoured  to  trace  the  steps 
by  which  men  acquired  each  main  portion  of  that  know- 


12  OF   IDEAS   IN   GENERAL. 

ledge  on  which  they  now  look  with  so  much  confidence 
and  satisfaction.  The  events  which  that  history  relates,  the 
speculations  and  controversies  which  are  there  described, 
and  discussions  of  the  same  kind,  far  more  extensive, 
which  are  there  omitted,  must  all  be  taken  into  our 
account  at  present,  as  the  prominent  and  standard 
examples  of  the  circumstances  which  attend  the  progress 
of  knowledge.  With  so  much  of  real  historical  fact 
before  us,  we  may  hope  to  avoid  such  views  of  the  pro- 
cesses of  the  human  mind  as  are  too  partial  and  limited, 
or  too  vague  and  loose,  or  too  abstract  and  unsubstantial, 
to  represent  fitly  the  real  forms  of  discovery  and  of  truth. 
Of  former  attempts,  made  with  the  same  view  of 
tracing  the  conditions  of  the  progress  of  knowledge,  that 
of  Bacon  is  perhaps  the  most  conspicuous :  and  his 
labours  on  this  subject  were  opened  by  his  book  on  the 
Advancement  of  Learning,  which  contains,  among  other 
matter,  a  survey  of  the  then  existing  state  of  knowledge. 
But  this  review  was  undertaken  rather  with  the  object  of 
ascertaining  in  what  quarters  future  advances  were  to  be 
hoped  for,  than  of  learning  by  what  means  they  were  to  be 
made.  His  examination  of  the  domain  of  human  know- 
ledge was  conducted  rather  with  the  view  of  discovering 
what  remained  undone,  than  of  finding  out  how  so  much 
had  been  done.  Bacon's  survey  was  made  for  the  purpose 
of  tracing  the  boundaries,  rather  than  of  detecting  the 
principles  of  knowledge.  "  I  will  now  attempt,"  he  says*, 
"  to  make  a  general  and  faithful  perambulation  of  learn- 
ing, with  an  inquiry  what  parts  thereof  lie  fresh  and 
waste,  and  not  improved  and  converted  by  the  industry  of 
man ;  to  the  end  that  such  a  plot  made  and  recorded  to 
memory,  may  both  minister  light  to  any  public  designa- 
tion, and  also  serve  to  excite  voluntary  endeavours." 
Nor  will  it  be  foreign  to  our  scheme  also  hereafter  to 
*  Achoncement  of  Learning  ^  b.  i.  p.  74. 


INTRODUCTION.  13 

examine  with  a  like  purpose  the  frontier  of  man's  intel- 
lectual estate.  But  the  object  of  our  perambulation  in 
the  first  place,  is  not  so  much  to  determine  the  extent  of 
the  field,  as  the  sources  of  its  fertility.  We  would  learn 
by  what  plan  and  rules  of  culture,  conspiring  with  the 
native  forces  of  the  bounteous  soil,  those  rich  harvests 
have  been  produced  which  fill  our  garners.  Bacon's 
maxims,  on  the  other  hand,  respecting  the  mode  in  which 
he  conceived  that  knowledge  was  thenceforth  to  be  cul- 
tivated, have  little  reference  to  the  failures,  still  less  to 
the  successes,  which  are  recorded  in  his  Review  of  the 
learning  of  his  time.  His  precepts  are  connected  with 
his  historical  views  in  a  slight  and  unessential  manner. 
His  philosophy  of  the  sciences  is  not  collected  from  the 
sciences  which  are  noticed  in  his  survey.  Nor,  in  truth, 
could  this,  at  the  time  when  he  wrote,  have  easily  been 
otherwise.  At  that  period,  scarce  any  branch  of  physics 
existed  as  a  science,  except  astronomy.  The  rules  which 
Bacon  gives  for  the  conduct  of  scientific  researches  are 
obtained,  as  it  were,  by  divination,  from  the  contempla- 
tion of  subjects  with  regard  to  which  no  sciences  as  yet 
were.  His  instances  of  steps  rightly  or  wrongly  made  in 
this  path,  are  in  a  great  measure  cases  of  his  own  devis- 
ing. He  could  not  have  exemplified  his  Aphorisms  by 
references  to  treatises  then  extant,  on  the  laws  of  nature ; 
for  the  constant  burden  of  his  exhortation  is,  that  men 
up  to  his  time  had  almost  universally  followed  an  erro- 
neous course.  And  however  we  may  admire  the  sagacity 
with  which  he  pointed  the  way  along  a  better  path,  we 
have  this  great  advantage  over  him ; — that  we  can  interro- 
gate the  many  travellers  who  since  his  time  have  journeyed 
on  this  road.  At  the  present  day,  when  we  have  under 
our  notice  so  many  sciences,  of  such  wide  extent,  so  well 
established ;  a  Philosophy  of  the  Sciences  ought,  it  must 
seem,  to  be  founded,  not  upon  conjecture,  but  upon  an 


14  OF    IDEAS   IN    GENERAL. 

examination  of  many  instances  ; — should  not  consist  of  a 
few  vague  and  unconnected  maxims,  difficult  and  doubt- 
ful.in  their  application,  but  should  form  a  system  of  which 
every  part  has  been  repeatedly  confirmed  and  verified. 

This  accordingly  it  is  the  purpose  of  the  present  work 
to  attempt.  But  I  may  further  observe,  that  as  my  hope 
of  making  any  progress  in  this  undertaking  is  founded 
upon  the  design  of  keeping  constantly  in  view  the  whole 
result  of  the  past  history  and  present  condition  of  science, 
I  have  also  been  led  to  draw  my  lessons  from  my  exam- 
ples in  a  manner  more  systematic  and  regular,  as  appears 
to  me,  than  has  been  done  by  preceding  writers.  Bacon, 
as  I  have  just  said,  was  led  to  his  maxims  for  the  promo- 
tion of  knowledge  by  the  sagacity  of  his  own  mind,  with 
little  or  no  aid  from  previous  examples.  Succeeding 
philosophers  may  often  have  gathered  useful  instruction 
from  the  instances  of  scientific  truths  and  discoveries 
which  they  adduced,  but  their  conclusions  were  drawn 
from  their  instances  casually  and  arbitrarily.  They  took 
for  their  moral  any  which  the  story  might  suggest.  Bat 
such  a  proceeding  as  this  cannot  suffice  for  us,  whose  aim 
is  to  obtain  a  consistent  body  of  philosophy  from  a  con- 
templation of  the  whole  of  Science  and  its  History.  For 
our  purpose  it  is  necessary  to  resolve  scientific  truths  into 
their  conditions  and  ingredients,  in  order  that  we  may  see 
in  what  manner  e*ach  of  these  has  been  and  is  to  be 
provided,  in  the  cases  which  we  may  have  to  consider. 
This  accordingly  is  necessarily  the  first  part  of  our  task  ' 
—to  analyse  scientific  truth  into  its  elements.  This  attempt 
will  occupy  the  earlier  portion  of  the  present  work ;  and 
will  necessarily  be  somewhat  long,  and  perhaps,  in  many 
parts,  abstruse  and  uninviting.  The  risk  of  such  an 
inconvenience  is  inevitable ;  for  the  inquiry  brings  before 
us  many  of  the  most  dark  and  entangled  questions  in 
which  men  have  at  any  time  busied  themselves.  And 


INTRODUCTION.  15 

even  if  these  can  now  be  made  clearer  and  plainer  than 
of  yore,  still  they  can  be  made  so  only  by  means  of  men- 
tal discipline  and  mental  effort.  Moreover  this  analysis 
of  scientific  truth  into  its  elements  contains  much,  both  in 
its  principles  and  in  its  results,  different  from  the  doctrines 
most  generally  prevalent  among  us  in  recent  times  :  but 
on  that  very  account  this  analysis  is  an  essential  part 
of  the  doctrines  which  I  have  now  to  lay  before  the 
reader :  and  I  must  therefore  crave  his  indulgence  towards 
any  portion  of  it  which  may  appear  to  him  obscure  or 
repulsive. 

There  is  another  circumstance  which  may  tend  to 
make  the  present  work  less  pleasing  than  others  on  the 
same  subject,  in  the  nature  of  the  examples  of  human 
knowledge  to  which  I  confine  myself;  all  my  instances 
being,  as  I  have  said,  taken  from  the  material  sciences. 
For  the  truths  belonging  to  these  sciences  are,  for  the 
most  part,  neither  so  familiar  nor  so  interesting  to  the 
bulk  of  readers  as  those  doctrines  which  belong  to  some 
other  subjects.  Every  general  proposition  concerning 
politics  or  morals  at  once  stirs  up  an  interest  in  men's 
bosoms,  which  makes  them  listen  with  curiosity  to  the 
attempts  to  trace  it  to  its  origin  and  foundation.  Every 
rule  of  art  or  language  brings  before  the  mind  of  culti- 
vated men  subjects  of  familiar  and  agreeable  thought, 
and  is  dwelt  upon  with  pleasure  for  its  own  sake  as  well 
as  on  account  of  the  philosophical  lessons  which  it  may 
convey.  But  the  curiosity  which  regards  the  truths  of 
physics  or  chemistry,  or  even  of  physiology  and  astro- 
nomy, is  of  a  more  limited  and  less  animated  kind. 
Hence,  in  the  mode  of  inquiry  which  I  have  prescribed 
to  myself,  the  examples  which  I  have  to  adduce  will  not 
amuse  and  relieve  the  reader's  mind  as  much  as  they 
might  do,  if  I  could  allow  myself  to  collect  them  from 
the  whole  field  of  human  knowledge.  They  will  have  in 


16  OF   IDEAS    IN    GENERAL. 

them  nothing  to  engage  his  fancy,  or  to  warm  his  heart. 
I  am  compelled  to  detain  the  listener  in  the  chilly  air 
of  the  external  world,  in  order  that  we  may  have  the 
advantage  of  full  daylight. 

But  although  I  cannot  avoid  this  inconvenience,  so  far 
as  it  is  one,  I  hope  it  will  be  recollected  how  great  are  the 
advantages  which  we  obtain  by  this  restriction.  We  are 
thus  enabled  to  draw  all  our  conclusions  from  doctrines 
which  are  universally  allowed  to  be  eminently  certain, 
clear,  and  definite.  The  portions  of  knowledge  to  which 
I  refer  are  well  known,  and  well  established  among  men. 
Their  names  are  familiar,  their  assertions  uncontested. 
Astronomy  and  geology,  mechanics  and  chemistry,  optics 
and  acoustics,  botany  and  physiology,  are  each  recognised 
as  large  and  substantial  collections  of  undoubted  truths. 
Men  are  wont  to  dwell  with  pride  and  triumph  on  the 
acquisitions  of  knowledge  which  have  been  made  in  each 
of  these  provinces ;  and  to  speak  with  confidence  of  the 
certainty  of  their  results.  And  all  can  easily  learn  in 
what  repositories  these  treasures  of  human  knowledge  are 
to  be  found.  When,  therefore,  we  begin  our  inquiry 
from  such  examples,  we  proceed  upon  a  solid  foundation. 
With  such  a  clear  ground  of  confidence,  we  shall  not  be 
met  with  general  assertions  of  the  vagueness  and  un- 
certainty of  human  knowledge ;  with  the  question,  what 
truth  is  and  how  we  are  to  recognise  it ;  with  complaints 
concerning  the  hopelessness  and  unprofitableness  of  such 
researches.  We  have,  at  least,  a  definite  problem  before 
us.  We  have  to  examine  the  structure  and  scheme,  not 
of  a  shapeless  mass*  of  incoherent  materials,  of  which  we 
doubt  whether  it  be  a  ruin  or  a  natural  wilderness,  but  of 
a  fair  and  lofty  palace,  still  erect  and  tenanted,  where 
hundreds  of  different  apartments  belong  to  a  common 
plan,  where  every  generation  adds  something  to  the 
extent  and  magnificence  of  the  pile.  The  certainty  and 


INTRODUCTION.  17 

the  constant  progress  of  science  are  things  so  unques- 
tioned, that  we  are  at  least  engaged  in  an  intelligible 
inquiry,  when  we  are  examining  the  grounds  and  nature 
of  that  certainty,  the  causes  and  laws  of  that  progress. 

To  this  inquiry,  then,  we  now  proceed.  And  in 
entering  upon  this  task,  however  our  plan  or  our  prin- 
ciples may  differ  from  those  of  the  eminent  philosophers 
who  have  endeavoured,  in  our  own  or  in  former  times,  to 
illustrate  or  enforce  the  philosophy  of  science,  we  most 
willingly  acknowledge  them  as  in  many  things  our 
leaders  and  teachers.  Each  reform  must  involve  its  own 
peculiar  principles,  and  the  result  of  our  attempts,  so  far 
as  they  lead  to  a  result,  must  be,  in  some  respects, 
different  from  those  of  former  works.  But  we  may  still 
share  with  the  great  writers  who  have  treated  this 
subject  before  us,  their  spirit  of  hope  and  trust,  their 
reverence  for  the  dignity  of  the  subject,  their  belief  in 
the  vast  powers  and  boundless  destiny  of  man.  And  we 
may  once  more  venture  to  use  the  words  of  hopeful 
exhortation,  with  which  the  greatest  of  those  who  have 
trodden  this  path  encouraged  himself  arid  his  followers 
when  he  set  out  upon  his  way. 

"  Concerning  ourselves  we  speak  not ;  but  as  touching 
the  matter  which  we  have  in  hand,  this  we  ask ; — that 
men  deem  it  not  to  be  the  setting  up  an  Opinion,  but  the 
performing  of  a  Work :  and  that  they  receive  this  as  a 
certainty ;  that  we  are  not  laying  the  foundations  of  any 
sect  or  doctrine,  but  of  the  profit  and  dignity  of  mankind. 
Furthermore,  that  being  well  disposed  to  what  shall 
advantage  themselves,  and  putting  off  factions  and  pre- 
judices, they  take  common  counsel  with  us,  to  the  end 
that  being  by  these  our  aids  and  appliances  freed  and 
defended  from  wanderings  and .  impediments,  they  may 
lend  their  hands  also  to  the  labours  which  remain  to  be 
performed :  and  yet  further,  that  they  be  of  good  hope ; 
VOL.  i.  c 


18  OF    IDEAS    IN    GENERAL. 

neither  imagine  to  themselves  this  our  Reform  as  some- 
thing of  infinite  dimension,  and  beyond  the  grasp  of 
mortal  man,  when  in  truth  it  is  the  end  and  true  limit  of 
infinite  errour;  and  is  by  no  means  unmindful  of  the 
condition  of  mortality  and  humanity,  not  confiding  that 
such  a  thing  can  be  carried  to  its  perfect  close  in  the 
space  of  one  single  age,  but  assigning  it  as  a  task  to  a 
succession  of  generations." 


CHAPTER  II. 
OF   FACTS  AND   THEORIES. 

1.  I  REGRET  very  much  that  I  must  begin  my  discus- 
sion by  questioning  the  validity  of  a  distinction  which  is 
usually  considered  to  be  clear  and  plain.  For  my  pur- 
pose is  to  establish  distinctions,  not  to  obliterate  them ; 
and  with  regard  to  such  contrasts  as  are  commonly 
recognised  among  men,  it  will  generally  be  my  business 
rather  to  point  out  their  real  import,  and  give  them  as 
much  clefiniteness  as  possible,  than  to  endeavour  to 
involve  them  in  doubt  and  confusion.  And,  indeed, 
though  I  am  compelled  at  first  to  expose  the  obscurity 
of  the  supposed  line  which  separates  Fact  and  Theory,  I 
shall  afterwards  have  to  show  that  the  contrast  which  we 
mark  by  these  terms  does  really  involve  an  antithesis 
which  is  the  foundation  of  the  whole  philosophy  of  know- 
ledge. 

Every  one  is  familiar  with  the  distinction  of  Fact  and 
Theory  as  commonly  understood.  Facts  offer  themselves 
to  our  senses  on  every  side :  ingenious  men  have  framed 
Theories,  that  is,  modes  of  mental  conception,  by  which 
the  facts  are  interpreted,  connected,  and  accounted  for. 
Every  moment  offers  us  examples  of  the  two.  The  day 


OF   FACTS   AND    THEORIES.  19 

dawns;  the  sun's  bright  edge  beams  over  the  distant 
hills;  that  is  the  fact.  The  theory  is  that  the  earth's 
surface  rolls  round  towards  the  sun,  and  thus  brings  him 
into  view.  The  dew-drops  hang  on  the  blade  and  the 
leaf;  their  globular  form  is  a  fact.  By  our  theory  we 
see  in  this  fact  a  mutual  attraction  of  the  minutest  por- 
tion of  the  water  which  composes  the  drops.  Each  drop, 
as  it  hangs  in  the  sunshine,  has  on  its  surface  a  bright 
spot  which  shifts  as  the  beholder  moves,  and  has  behind 
it  another  bright  speck  which  falls  on  some  neighbouring 
object.  These  facts  our  theories  make  us  contemplate 
as  the  reflected  and  refracted  light  of  the  sun.  The 
plant  thus  hung  with  dew  exhibits  to  us  its  leaves  and 
flowers,  but  in  our  minds  we  compare  it  with  other  plants 
in  which  the  leaves  and  flowers  are  more  or  less  different ; 
we  consider  these  facts  as  indicating  the  relation  of  this 
particular  plant  to  some  wider  family  of  the  vegetable 
system,  such  as  in  our  theory  we  have  arranged  it.  Or 
if  we  are  acquainted  with  the  plants  of  other  regions,  we 
may  see  in  the  existence  and  features  of  such  a  plant  the 
confirmation  of  a  theory  by  which  we  look  upon  some 
portion  of  our  vegetable  population  as  strangers  wandered 
hither  from  a  distant  land. 

2.  In  all  these  cases,  the  distinction  between  the  fact 
as  it  presents  itself  to  our  senses  and  the  theoretical 
view,  seems  at  first  sight  plain  enough.  Yet  a  little  con- 
sideration may  show  us  that  this  distinction  is  not  in 
every  case  quite  clear.  Is  it  not  a  fact  as  well  as  a 
theory  that  we  see  the  light  reflected  from  the  surface  of 
a  dew-drop,  and  do  we  not  by  our  common  language 
acknowledge  it  to  be  so  ?  And  is  not  the  refraction  of 
the  light  through  the  water  as  much  a  fact  as  its  reflection 
from  the  surface?  Does  not  the  manner  in  which  the 
drop  hangs  from  the  leaf  show  that  it  is  a  fact  that  the 
particles  of  water  adhere  to  or  attract  each  other?  Is  not 

C  2 


20  OF    IDEAS    IN    GENERAL. 

tins  as  much  a  fact  as  the  globular  form  of  the  drops,  or 
indeed  more  so,  for  the  drops  are  riot  strictly  globular? 
That  they  are  not  so,  we  learn  from  theory,  and  thus 
our  theory  corrects  our  facts.  Is  not  the  greater  or  less 
resemblance  of  one  plant  to  another  a  fact  ?  and  is  not, 
therefore,  a  classification,  which  is  merely  a  collection  of 
such  resemblances,  a  fact  also  ?  And  if  the  doctrine  of 
the  derivation  of  any  particular  plant  from  one  region  to 
another  be  a  true  theory,  is  it  not  a  fact  on  that  very 
account  ? 

And  with  regard  to  the  first  mentioned  of  the  above 
cases,  the  theoretical  motion  of  the  earth,  is  not  that  also 
a  fact,  if  the  theory  be  true  ?  It  may  be  said  that  the 
theory  contradicts  the  facts  as  noticed  by  our  senses. 
But  that  our  senses  may  misinform  us  respecting  facts, 
we  easily  see.  When  we  glide  along  smooth  water  in 
a  barge,  our  senses  inform  us  that  the  shore  moves  away 
from  us ;  but  we  know  the  fact  to  be  otherwise.  And  if 
the  motion  of  the  barge  be  the  fact  in  this  case,  is  not 
the  motion  of  the  earth,  by  which  the  sun's  rising  is  pro- 
duced, a  fact  no  less  ? 

Again,  if  it  were  said  that  that  is  a  fact  which  our 
senses  perceive,  the  question  must  be  asked,  whose  senses? 
One  man  watches  the  stars  all  the  night,  and  sees  them 
describe  circles  about  the  pole ;  another  looks  at  them 
carelessly  and  at  intervals,  and  sees  no  circles.  Is  not 
the  diurnal  circular  motion  of  the  stars  a  fact  ?  Again, 
a  man  may  rightly  apprehend  the  motion  of  the  stars  for 
one  night,  but  may  not  notice  the  motion  of  the  moon 
among  the  stars  from  night  to  night.  Another  man 
notices  this  latter  motion  also :  to  him  the  moon's 
monthly  circuit  through  the  heavens  is  a  fact.  And 
again,  to  another  observer,  more  vigilant,  the  annual 
motion  of  the  sun  in  the  ecliptic  is  a  fact  just  as  much 
as  the  monthly  motion  of  the  moon  in  her  orbit.  For 


OF    FACTS    AND    THEORIES.  21 

the  only  difference  is,  that  the  moon's  light  quenches 
only  the  smaller  stars  in  her  neighbourhood,  while  the 
sun  obliterates  all.  And  thus  what  is  matter  of  theory 
to  one  observer  is  matter  of  fact  to  another. 

Is  it  not,  indeed,  evident  that  a  theory,  if  it  be  true, 
is  on  that  very  account  a  fact?  All  the  great  theories 
which  have  successively  been  established  in  the  world, 
are  now  thought  of  as  facts.  Is  not  the  motion  of  the 
earth  round  the  sun  a  fact  ?  Is  not  the  elliptical  form 
of  the  planets'  orbits  a  fact  ?  Is  not  the  attraction  of  the 
sun  upon  the  planets  a  fact  ?  Is  not  the  circulation  of 
the  blood  a  fact  ?  The  definite  and  multiple  proportions 
of  the  elements  of  bodies,  which  make  up  what  is  com- 
monly called  the  atomic  theory,  are  not  they  facts? 

Thus,  the  opposition  of  fact  and  theory — a  contrast 
which  at  first  appeared  so  broad  and  plain — as  we  examine 
it,  becomes  wavering,  obscure,  and  doubtful.  The  line  of 
demarcation  is  invisible ;  the  application  of  the  distinc- 
tion full  of  difficulty.  That  which  is  a  fact  under  one 
aspect  is  a  theory  under  another.  The  most  recondite 
theories,  when  firmly  established,  are  accepted  as  facts ; 
the  simplest  facts  appear  to  involve  something  of  the 
nature  of  theory. 

3.  But  yet,  in  what  has  been  said,  something  of  a 
difference  between  fact  and  theory  still  remains  apparent. 
It  is  only  when  theories  are  firmly  established,  and  recog- 
nised as  indisputably  true,  that  they  become  facts,  The 
view,  originally  theoretical,  becomes  at  length  so  con- 
vincing, that  it  occurs  to  us  as  the  most  natural  view,  and 
then  it  is  theoretical  no  longer.  The  interpretation  of 
appearances,  which  was  at  first  a  novelty  and  an  effort, 
becomes  at  last  so  familiar  that  we  are  not  conscious  of 
it ;  and  then  the  distinction  of  theory  and  fact,  in  that 
instance,  melts  away.  Theory  is  some  interpretation 
of  phenomena,  or  inference  from  them,  which  we  make 


22  OF    IDEAS   IN    GENERAL. 

by  a  conscious  act  of  thought,  adding  some  new  form  of 
conception  to  that  which  at  first  offers  itself.  And  as 
the  doubt,  and  the  effort,  and  the  consciousness  of  the 
mental  act  gradually  depart,  the  theory  is  a  theory  no 
longer,  but  becomes  a  fact. 

And  thus,  as  we  become  more  and  more  familiar  with 
sound  theoretical  views,  such  views  become  to  us  as 
really  facts  as  those  which  are  most  obvious  to  the  senses. 
The  astronomer,  constantly  observing  the  moon,  and  de- 
termining from  her  apparent  her  real  motions,  sees 
that  she  is  drawn  by  the  earth,  as  clearly  as  a  common 
spectator  sees  the  needle  drawn  by  the  magnet.  That 
which  is  intellectual  effort  to  others  is  unconscious  habit 
in  him.  He  sees  the  true  motion  in  the  apparent,  and 
separates  the  compound  course  into  the  simple  paths,  with 
no  more  doubt  than  the  voyager  feels  when,  in  judging  of 
the  course  of  a  distant  ship,  he  allows  for  the  motion  of 
his  own  vessel,  and  for  his  own  movements  as  he  walks 
the  deck.  And  as  this  true  motion  of  the  paths  of  the 
earth  and  moon,  which  is  to  him  an  habitual  and  ine- 
vitable interpretation  of  their  visible  changes,  is  thus  a 
fact,  the  mutual  attraction  of  the  two  bodies,  which  is 
but  a  further  interpretation,  equally  inevitable,  of  those 
motions,  is  also  a  fact  to  him :  while  to  those  less  accus- 
tomed to  such  interpretations,  and  who,  therefore,  cannot 
apply  them  without  a  conscious  act  of  thought,  such  a 
view  of  the  case,  even  when  accepted  as  true,  is  more 
properly  described  as  theory. 

4.  In  this  instance,  the  doctrine  of  which  I  have 
spoken,  the  attraction  which  the  earth  exerts  upon  the 
moon,  would  be  termed  a  theory  by  most  persons  ;  because 
those  to  whom  this  is  a  familiar  and  simple  inference  from 
the  phenomena  are  only  a  few  accomplished  astronomers. 
But,  in  other  similar  cases,  many,  or  most  persons,  per- 
form a  similar  act  of  interpretation,  without  being  con- 


OF   FACTS    AND    THEORIES.  23 

scions  of  it.  When  we  assert  that  the  magnet  draws  the 
needle,  we  see  only  the  motion  of  the  needle  which  oc- 
curs when  the  magnet  is  brought  into  its  neighbourhood. 
It  is  by  an  act  of  our  own  minds  that  we  ascribe  this 
motion  to  a  force.  That  in  this  case  a  force  is  exerted 
upon  the  needle,  such  as  we  could  by  our  volition  exert, 
is  our  unconscious  interpretation  of  the  phenomena,  and 
is  hence  received  by  us  as  a  fact. 

5.  But  it  is  not  in  such  cases  only  that  we  interpret 
phenomena  in  our  own  way,  without  being  conscious  of 
what  we  do.  We  see  a  tree  at  a  distance,  and  judge  it 
to  be  a  chestnut  or  a  lime  ;  yet  this  is  only  an  inference 
from  the  colour  or  form  of  the  mass,  according  to  precon- 
ceived classifications  of  our  own.  Our  lives  are  full  of 
such  unconscious  interpretations.  The  farmer  recognises 
a  good  or  bad  soil ;  the  artist  a  picture  of  a  favourite 
master ;  the  geologist  a  rock  of  a  known  locality,  as  we 
recognise  the  faces  and  voices  of  our  friends ;  that  is,  by 
judgments  formed  on  what  we  see  and  hear ;  but  judg- 
ments in  which  we  do  not  analyse  the  steps,  or  distinguish 
the  inference  from  the  appearance.  And  in  these  mix- 
tures of  observation  and  inference,  we  speak  of  the 
judgment  thus  formed,  as  a  fact  directly  observed. 

Even  in  the  case  in  which  our  perceptions  appear  to 
be  most  direct,  and  least  to  involve  any  interpretations  of 
our  own, — in  the  simple  process  of  seeing, — who  does 
not  know  how  much  we,  by  an  act  of  the  mind, -add  to 
that  which  our  senses  receive  ?  Does  any  one  fancy  that 
he  sees  a  solid  cube  ?  It  is  easy  to  show  that  the  solidity 
of  the  figure,  the  relative  position  of  its  faces  and  edges 
to  each  other,  are  inferences  of  the  spectator ;  no  more 
conveyed  to  his  conviction  by  the  eye  alone,  than  they 
would  be  if  he  were  looking  at  a  painted  representation  of 
a  cube.  The  scene  of  nature  is  a  picture  without  depth 
of  substance,  no  less  than  the  scene  of  art;  and  in  the 


24  OF    IDEAS    IN    GENERAL. 

one  case  as  in  the  other,  it  is  the  mind  which,  by  an  act 
of  its  own,  discovers  that  colour  and  shape  denote  dis- 
tance and  solidity.  Most  men  are  unconscious  of  this 
perpetual  habit  of  reading  the  language  of  the  external 
world,  and  translating  as  they  read.  The  draughtsman, 
indeed,  is  compelled,  for  his  purposes,  to  return  back  in 
thought  from  the  solid  bodies  which  he  has  inferred,  to 
the  shapes  of  surface  which  he  really  sees.  He  knows 
that  there  is  a  mask  of  theory  over  the  whole  face  of 
nature,  if  it  be  theory  to  infer  more  than  we  see.  But 
other  men,  unaware  of  this  masquerade,  hold  it  to  be  a 
fact  that  they  see  cubes  and  spheres,  spacious  apartments 
and  winding  avenues.  And  these  things  are  facts  to 
them,  because  they  are  unconscious  of  the  mental  opera- 
tion by  which  they  have  penetrated  nature's  disguise. 

And  thus  we  still  have  an  intelligible  distinction  of 
fact  and  theory,  if  we  consider  theory  as  a  conscious,  and 
fact  as  an  unconscious  inference  from  the  phenomena 
which  are  presented  to  our  senses. 

6.  Yet  still  the  distinction  thus  stated  is  far  from 
being  rigorous  and  permanent,  as,  in  truth,  we  have  already 
seen  that  in  practice  it  is  very  precarious  and  obscure. 
The  difference  of  conscious  and  unconscious  acts  is  by  no 
means  strongly  marked.  Education,  habit,  the  degree  of 
self-observation,  the  circumstances  of  the  case,  all  serve 
to  make  the  person  unconscious  or  conscious  of  mental 
acts  in  innumerable  degrees.  The  draughtsman  sees  in 
nature  features  and  outlines  which  others  do  not  see. 
The  practised  astrologer  sees  the  moon  walk  from  house 
to  house  in  her  path,  as  he  sees  his  friend  walk  from  house 
to  house  in  the  street ;  the  beginner  in  the  study  sees  this 
with  conscious  effort.  But  one  of  these  habits  gradually 
passes  into  the  other.  The  distinction  of  conscious  and 
unconscious  acts  of  thought  fades  away  as  we  examine  it. 
We  may  walk  or  talk,  as  well  as  see,  without  conscious 


OF    FACTS   AND    THEORIES.  25 

effort ;  yet  walking  and  talking  imply  acts  of  thought,  as 
we  perceive  when  we  walk  on  a  rugged  path,  or  talk  in 
a  foreign  language.  Hence  if  this  greater  or  less  consci- 
ousness of  our  own  internal  act  be  all  that  distinguishes 
fact  from  theory,  we  must  allow  that  the  distinction  is  still 
untenable.  The  boundary-line  again  melts  away;  the 
difference  is  unsubstantial ;  the  opposition  loses  its  signi- 
ficance as  we  examine  it. 

Still  there  appears  to  be  something  real  in  this  anti- 
thesis, and  we  must  return  to  the  examination  of  it  under 
another  form. 


CHAPTER  III. 
OF   SENSATIONS   AND   IDEAS. 

1.  IT  has  appeared  that  facts  as  well  as  theories  in- 
volve some  act  of  the  mind.  But  it  is  also  clear  that  they 
must  involve  something  else  besides  an  act  of  the  mind. 
If  we  must  exercise  an  act  of  thought  in  order  to  see  force 
exerted,  or  orbits  described  by  bodies  in  motion,  or  even 
in  order  to  see  bodies  in  space,  and  to  distinguish  one 
kind  of  object  from  another,  still  the  act  of  thought  alone 
does  not  make  these  objects.  There  must  be  something 
besides,  on  which  the  thought  is  exerted.  A  colour,  a 
form,  a  sound,  are  not  produced  by  the  mind,  however 
they  may  be  moulded,  combined,  and  interpreted  by  our 
mental  acts.  A  philosophical  poet  has  spoken  of 

All  the  world 

Of  eye  and  ear,  both  what  they  half  create, 
And  what  perceive. 

But  it  is  clear  that  though  they  half  create,  they  do  not 
wholly  create ;  there  must  be  an  external  world  of  colour 
and  sound  to  give  impressions  to  the  eye  and  ear,  as 
well  as  internal  powers  by  which  we  perceive  what  is 


26  OF   IDEAS   IN    GENERAL. 

offered  to  those  organs.  The  mind  is  in  some  way  passive 
as  well  as  active:  there  are  sensations  as  well  as  acts  of 
thought ;  objects  without,  as  well  as  faculties  within. 

2.  Indeed  this  is  so  far  generally  acknowledged,  that 
according  to  common  apprehension,  the  mind  is  passive 
rather  than  active  in  acquiring  the  knowledge  which  it 
receives  concerning  the  material  world.    Its  sensations  are 
generally  considered  as  more  evident  than  its  operations. 
The  world  without  is  held  to  be  more  clearly  real  than 
the  faculties  within.     That  there  is  something  different 
from  ourselves,  something  external  to  us,  something  in- 
dependent of  us,  something  which   no  act  of  our  minds 
can  make  or  can  destroy,  is  held  by  all  men  to  be  at 
least  as  evident  as  that  our  minds  exert  any  effectual  pro- 
cess in  modifying  and  appropriating  the  impressions  made 
upon   them.      Most    persons  are   more  likely  to  doubt 
whether  the  mind  be   always    active  in    contemplating 
external  objects,  than  whether  it  be  always  passive  in 
perceiving  them. 

This  question,  however,  we  have  already,  in  some  mea- 
sure, answered ;  for  we  have  shown,  that  in  many  in- 
stances where  we  are  at  the  time  unconscious  of  what  we 
do,  we  are  combining,  interpreting,  reasoning  from  the 
appearances  which  we  have  before  our  eyes ;  and  that 
without  this  operation  we  cannot  know  anything,  nor  even 
recognise  any  single  body  as  existing  in  the  space  about  us. 
This  view  of  the  process  of  perception  will  be  further  pro- 
secuted hereafter ;  but,  in  the  mean  time,  we  have,  it  may 
be  hoped,  made  it  appear  that  in  his  apprehension  of  the 
objects  which  nature  presents  to  him,  man  is  both  active 
and  passive :  that  he  has  both  Ideas  and  Sensations. 

3.  I   use    the    term  Idea   here  to    designate    those 
inevitable  general  relations  which  are  imposed  upon  our 
perceptions  by  acts  of  the  mind,  and  which  are  different 
from  anything  which  our  senses  directly  offer  to  us.    Thus 


OF   SENSATIONS   AND   IDEAS.  27 

we  see  various  shades,  and  colours,  and  shapes  before  us ; 
but  the  outlines  by  which  they  are  separated  into  distinct 
objects,  the  conception  by  which  they  are  considered  as  solid 
bodies>  at  various  distances  from  us ;  these  elements  are  not 
ministered  by  the  senses,  but  supplied  by  the  mind  itself. 
And  in  drawing  the  outlines  of  bodies,  in  placing  them  at 
different  distances  from  us,  the  mind  proceeds  in  accord- 
ance with  certain  necessary  general  relations  which  are 
involved  in  the  Idea  of  Space.  In  like  manner  when,  seeing 
the  motions  of  a  needle  towards  a  magnet,  we  conceive  an 
attractive  force  exerted  and  obeyed,  we  form  this  concep- 
tion by  referring  these  motions  to  the  Idea  of  Cause. 

Our  sensations  are  constantly  apprehended  in  subor- 
dination to  such  ideas  as  these.  And  ideas  of  this  wide 
and  comprehensive  nature,  such  as  space  and  time,  num- 
ber and  figure,  cause  and  resemblance,  which  are  the 
source  of  an  innumerable  series  of  more  limited  concep- 
tions, I  term  Fundamental  Ideas ;  and  I  shall  hereafter 
endeavour  to  enumerate  and  analyse  some  of  the  most 
important  of  them. 

4.  I  am  thus  using  the  term  Idea  in  a  very  wide  sense. 
But  yet  this  use  of  it  is  far  more  limited  than  that  which 
occurs  in  common  language.  For  I  restrict  its  applica- 
tion to  the  relations  and  conditions  which  are  imposed  on 
our  sensations  through  the  activity  of  the  mind ;  and 
thus  I  do  not  apply  the  term  to  any  impressions  made 
upon  the  mind  in  virtue  of  its  passive  nature  merely. 
Whereas  the  term  idea  has  often  been  used  for  almost  all 
imaginable  results  of  our  passive  and  active  powers  com- 
bined. If  we  speak  of  an  idea  of  any  existing  object,  as 
for  example,  of  St.  Paul's  cathedral,  we  denote  by  this 
use  of  the  term,  a  combination  of  various  recollected  im- 
pressions of  form  and  colour,  as  well  as  order  and  sym- 
metry, and  we  thus  include  in  the  word  a  mixture  of 
Sensations,  as  well  as  Ideas  in  the  more  exact  sense  which 


28  OF    IDEAS    IN    GENERAL. 

I  would  assign  to  the  term.  But  the  word  thus  applied 
appears  to  answer  no  purpose  of  analysis  ;  or  at  least  not 
the  purpose  which  we  have  here  in  view.  The  distinction 
of  Sensations  which  the  mind  passively  receives,  and  Ideas 
which  it  actively  employs,  is  of  the  highest  importance  in 
order  to  the  prosecution  of  our  investigations.  And  in 
order  that  we  may  keep  this  difference  steadily  before  us, 
I  shall  trust  to  be  allowed  the  liberty  of  assigning  to  these 
terms,  in  these  pages,  this  definite  and  constant  sense. 
I  must  now  further  consider  the  distinction  and  indepen- 
dence of  these  two  elements. 


CHAPTER  IV. 

OF  THE  DIFFERENCE  AND  OPPOSITION  OF 
SENSATIONS  AND  IDEAS. 

1.  Ideas  and  Sensations  are  distinct* — Thus  Ideas  are 
the  active,  Sensations  the  passive  element  of  our  minds. 
But  it  may  be  urged,  that  it  is  impossible  to  make  such  a 
separation  of  our  consciousness.  There  are,  as  we  have 
already  said,  few  cases,  if  any,  in  which  the  mind  is 
entirely  passive ;  some  act  of  the  mind  accompanies  the 
reception  of  our  most  tranquil  perceptions.  And  on  the 
other  hand,  it  is  clear  that  no  act  of  the  mind  can  be  con- 
ceived without  some  impression  previously  made  on  the 
senses.  Without  the  use  of  sight  and  touch,  where 
would  be  our  idea  of  space,  or  number,  or  resemblance, 
or  cause?  And  thus,  it  may  be  said,  ideas  (in  our  sense 
of  the  term)  without  sensations,  and  sensations  without 
ideas,  are  altogether  idle  and  imaginary  hypotheses. 
They  can  nowhere  be  found  in  reality.  And  a  distinction 
where  separation  is  impossible  can  be  of  no  use  or  value. 

To  this  we  reply,  that  although  it  is  impossible  com- 
pletely to  separate,  in  any  actual  cases,  sensations  and 


OPPOSITION    OP    SENSATIONS   AND    IDEAS.  29 

ideas,  nevertheless  tlie  distinction  is  real,  and  the  oppo- 
sition of  the  two  is  "a  principle  of  the  most  essential  im- 
portance in  all  philosophy.  And  this  principle  we  must 
endeavour  to  illustrate  further. 

The  distinction  has  constantly  exercised  a  very  im- 
portant influence  on  the  speculations  respecting  the  nature 
of  knowledge  in  which  men  have  employed  themselves  in 
all  ages ;  and  in  the  course  of  these  speculations  it  has 
been  illustrated  by  means  of  various  images.  One  of  the 
most  ancient  of  these,  and  one  still  very  instructive,  is 
that  which  speaks  of  the  sensations  as  the  matter,  and 
the  ideas  as  the  form  of  our  knowledge  :  just  as  ivory 
is  the  matter,  and  a  cube  the  form,  of  a  die.  And  this 
comparison  may  at  least  show  us  how  little  force  there  is 
in  the  objection  just  stated,  that  sensations  and  ideas  are 
not  separable  in  fact,  and  therefore  that  their  separation 
in  our  reasonings  can  be  of  no  service.  For  the  same  is 
the  case  with  respect  to  matter  and  form.  These  two 
things  cannot,  by  any  means,  be  detached  from  each 
other.  The  ivory  must  have  some  form ;  if  not  a  cube, 
a  sphere,  or  some  other.  The  cube,  in  order  to  be  a  cube, 
must  be  of  some  material  or  other.  A  figure  without 
matter  is  merely  a  geometrical  conception; — an  idea. 
Matter  without  figure  is  a  mere  abstract  term ; — a  sup- 
posed union  of  sensible  qualities  which,  so  insulated  from 
others,  cannot  exist.  Yet  the  distinction  of  matter  and 
form  is  real,  for  it  is  clear  and  plain  as  a  subject  of  con- 
templation. And  it  is  by  no  means  useless.  For  the 
speculations  which  treat  of  materials  are  very  widely 
separated  from  those  which  treat  of  figure.  On  each 
subject  there  may  be  much  to  be  said ;  and  the  two 
subjects  would  be,  through  their  whole  extent,  distinct. 
The  researches  concerning  the  two  may  involve  principles 
as  different,  for  example,  as  the  principles  of  chemistry  and 
geometry.  If,  therefore,  we  were  to  refuse  to  consider  the 


30  OF   IDEAS   IN   GENERAL. 

matter  and  the  form  of  bodies  separately,  because  we 
cannot  exhibit  matter  and  form  separately,  we  should 
shut  the  door  to  all  philosophy  on  such  subjects.  And 
the  same  is  the  case  with  the  analogous  instance  of  sensa- 
tions and  ideas. 

2.  Ideas  are  not  Transformed  Sensations. — In  a  certain 
school  of  speculators  there  has  existed  a  disposition  to 
derive  all  our  ideas  from  our  sensations,  the  term  idea 
having  been  used  in  its  wider  sense,  so  as  to  include  all 
modifications  and  limitations  of  our  Fundamental  Ideas. 
The  doctrines  of  this  school  have  been  summarily 
expressed  by  saying  that  "  every  idea  is  a  transformed 
sensation."  Now,  even  supposing  this  assertion  to  be 
exactly  true,  we  easily  see,  from  what  has  been  said,  how 
little  we  are  likely  to  answer  the  ends  of  philosophy,  by 
putting  forward  such  a  maxim  as  one  of  primary  import- 
ance. For  we  might  say,  in  like  manner,  that  every 
statue  is  but  a  transformed  block  of  marble,  or  every 
edifice  but  a  collection  of  transformed  stones.  But 
what  would  these  assertions  avail  us,  if  our  object  were  to 
trace  the  rules  of  art  by  which  beautiful  statues  were 
formed,  or  great  works  of  architecture  erected  ?  The 
question  naturally  occurs,  What  is  the  nature,  the  prin- 
ciple, the  law  of  this  transformation?  In  what  faculty 
resides  the  transforming  power?  What  train  of  ideas 
of  beauty,  and  symmetry,  and  stability,  in  the  mind  of 
the  statuary  or  the  architect,  has  produced  those  great 
works  which  mankind  look  upon  as  among  their  most 
valuable  possessions ; — the  Apollo  of  the  Belvedere,  the 
Parthenon, -the  Cathedral  of  Cologne  ?  When  this  is  what 
we  want  to  know,  how  are  we  helped  by  learning  that  the 
Apollo  is  of  Parian  marble,  or  the  Cathedral  of  basaltic 
stone  ?  We  must  know  much  more  than  this,  in  order 
to  acquire  any  insight  into  the  principles  of  statuary  or  of 
architecture.  In  like  manner,  in  order  that  we  may 


OPPOSITION    OF   SENSATIONS   AND   IDEAS.  31 

make  any  progress  in  the  philosophy  of  knowledge,  which 
is  our  purpose,  we  must  endeavour  to  learn  something 
further  respecting  ideas  than  that  they  are  transformed 
sensations,  even  if  they  were  this. 

But,  in  reality,  the  assertion  that  our  ideas  are  trans- 
formed sensations,  is  erroneous  as  well  as  frivolous.  For 
it  conveys,  and  is  intended  to  convey,  the  opinion  that 
our  sensations  have  one  form  which  properly  belongs  to 
them ;  and  that,  in  order  to  become  ideas,  they  are  con- 
verted into  some  other  form.  But  the  truth  is,  that  our 
sensations,  of  themselves,  without  some  act  of  the  mind, 
such  as  involves  what  we  have  termed  an  idea,  have  no 
form.  We  cannot  see  one  object  without  the  idea  of 
space ;  we  cannot  see  two  without  the  idea  of  resem- 
blance or  difference ;  and  space  and  difference  are  not 
sensations.  Thus,  if  we  are  to  employ  the  metaphor  of  mat- 
ter and  form,  which  is  implied  in  the  expression  to  which 
I  have  referred,  our  sensations,  from  their  first  reception, 
have  their  form  not  changed,  but  given  by  our  ideas. 
Without  the  relations  of  thought  which  we  here  term 
ideas,  the  sensations  are  matter  without  form.  Matter 
without  form  cannot  exist :  and  in  like  manner  sensations 
cannot  become  perceptions  of  objects,  without  some  forma- 
tive power  of  the  mind.  By  the  very  act  of  being  received 
as  perceptions,  they  have  a  formative  power  exercised 
upon  them,  the  operation  of  which  might  be  expressed 
by  speaking  of  them,  not  as  transformed,  but  simply  as 
formed; — as  invested  with  form,  instead  of  being  the 
mere  formless  material  of  perception.  The  word  inform, 
according  to  its  Latin  etymology,  at  first  implied  this 
process  by  which  matter  is  invested  with  form.  Thus 
.Virgil*  speaks  of  the  thunderbolt  as  informed  by  the 

*  Ferrum  exercebant  vasto  Cyclopes  in  Antro 

Brontesque  Steropesque  et  nudus  membra  Pyracmon  ; 
His  informattim  manibus,  jam  parte  polita 
Fulmen  erat.-~-<&.  viii.  424. 


32  OF   IDEAS   IN   GENERAL. 

hands  of  Brontes,  and  Steropes,  and  Pyracmon.  And 
Dryden  introduces  the  word  in  another  place  : — 

Let  others  better  mould  the  running  mass 
Of  metals,  or  inform  the  breathing  brass. 

Even  in  this  use  of  the  word  the  form  is  something 
superior  to  the  brute  matter,  and  gives  it  a  new  signi- 
ficance and  purpose.  And  hence  the  term  is  again  used 
to  denote  the  effect  produced  by  an  intelligent  principle 
of  a  still  higher  kind : — 

He  informed 

This  ill-shaped  body  with  a  daring  soul. 

And  finally  even  the  soul  itself,  in  its  original  condition, 
is  looked  upon  as  matter,  when  viewed  with  reference  to 
education  and  knowledge,  by  which  it  is  afterwards 
moulded ;  and  hence  these  are,  in  our  language,  termed 
information.  If  we  confine  ourselves  to  the  first  of  these 
three  uses  of  the  term,  we  may  correct  the  erroneous 
opinion  of  which  we  have  just  been  speaking,  and  retain 
the  metaphor  by  which  it  is  expressed,  by  saying,  that 
ideas  are  not  transformed,  but  informed  sensations. 

3.  Subjective  and  Objective. — There  is  another  mode  of 
expressing  the  distinction  of  our  sensations  and  our 
ideas,  which  has  been  often  used  by  writers  on  such 
topics,  although,  in  our  own  country,  of  late  years,  it  has 
not  been  familiar  to  general  readers.  According  to  the 
technical  language  of  ancient  philosophy,  any  one's  quali- 
ties and  acts  are  attributes  of  which  he  is  the  subject; 
and  thus  the  mind  is  the  subject  to  which  its  own  ideas 
and  operations  appertain.  But  these  ideas  are  employed 
upon  external  objects,  and  from  external  objects  all  his 
sensations  proceed.  Hence  that  part  of  man's  mental 
occupation  which  springs  from  the  faculties  and  operations 
of  his  own  mind  is  subjective,  while  that  which  flows  in 
upon  him  from  the  world  external  to  him  is  objective. 
And  as  in  his  contemplation  of  nature  there  is  always 


OPPOSITION    OF    SENSATIONS    AND    IDEAS.  33 

some  act  of  thought  which  depends  ou  himself,  and 
some  matter  of  thought  which  is  independent  of  him, 
there  is  in  every  part  of  his  knowledge  a  subjective  and 
an  objective  element. 

This  phraseology  is  very  familiar  in  the  philosophical 
writers  of  Germany  and  France,  and  is  not  uncommon  in 
every  age  of  our  own  literature.  But  whether  or  no  we 
think  fit  to  adopt  these  terms,  the  opposition  which  they 
imply  is  one  of  essential  and  fundamental  importance,  in 
all  our  speculations  concerning  the  nature  of  knowledge. 
We  may  express  the  opposition  in  what  terms  we  please  ; 
we  may  speak,  for  instance,  of  internal  and  external 
sources  of  our  knowledge ;  of  the  world  within  and  the 
world  without  us;  of  man  and  nature;  of  ideas  and  ex- 
perience ;  and  of  many  other  antitheses.  But,  in  what- 
ever way  we  denote  the  contrast  of  the  subjective  and 
objective  part  of  our  speculations,  the  distinction  is  real 
and  solid,  and  we  shall  hereafter  see  how  essential  the 
principle  of  this  contrast  is,  in  order  to  express  the  laws 
of  the  successful  prosecution  of  knowledge. 

The  combination  of  the  two,  of  ideas  and  experience, 
is,  as  we  shall  see,  necessary,  in  order  to  give  us  any 
knowledge  of  the  external  world,  any  insight  into  the 
laws  of  nature.  Different  persons,  according  to  their 
mental  habits  and  constitution,  may  be  inclined  to  dwell 
by  preference  upon  one  or  the  other  of  these  two  ele- 
ments. But  no  knowledge  can  exist  without  the  prac- 
tical union  of  the  two,  nor  any  philosophy  without  their 
speculative  separation.  It  may,  perhaps,  interest  the 
reader  to  see  this  combination  and  this  opposition  illus- 
trated in  the  intercourse  of  two  eminent  men  of  genius 
of  modern  times,  Gb'the  and  Schiller. 

Gb'the  himself  gives  us  the  account  to  which  I  refer, 
in  his  history  of  the  progress  of  his  speculations  concern- 
ing the  metamorphosis  of  plants;  a  mode  of  viewing  their 
VOL.  i.  D 


34  OF  IDEAS   IN   GENERAL. 

structure  by  which  he  explained,  in  a  very  striking  and 
beautiful  manner,  the  relations  of  the  different  parts  of  a 
plant  to  each  other ;  as  has  been  narrated  in  the  History 
of  the  Inductive  Sciences.  Gb'the  felt  a  delight  in  the 
passive  contemplation  of  nature,  unmingled  with  the 
desire  of  reasoning  and  theorizing;  a  delight  such  as 
naturally  belongs  to  those  poets  who  merely  embody  the 
images  which  a  fertile  genius  suggests,  and  do  not  mix 
with  these  pictures,  judgments  and  reflections  of  their 
own.  Schiller,  on  the  other  hand,  both  by  his  own  strong 
feeling  of  the  value  of  a  moral  purpose  in  poetry,  and  by 
his  adoption  of  a  system  of  metaphysics  in  which  the  sub- 
jective element  was  made  very  prominent,  was  well  dis- 
posed to  recognize  fully  the  authority  of  ideas  over 
external  impressions. 

Gb'the  for  a  time  felt  a  degree  of  estrangement  to- 
wards Schiller,  arising  from  this  contrariety  in  their  views 
and  characters.  But  on  one  occasion  they  fell  into  dis- 
cussion on  the  study  of  natural  history;  and  Gb'the 
endeavoured  to  impress  upon  his  companion  his  persua- 
sion that  nature  was  to  be  considered,  not  as  composed 
of  detached  and  incoherent  parts,  but  as  active  and  alive, 
and  unfolding  herself  in  each  portion,  in  virtue  of  prin- 
ciples which  pervade  the  whole.  Schiller  objected  that 
no  such  view  of  the  objects  of  natural  history  had  been 
pointed  out  by  observation,  the  only  guide  which  the 
natural  historians  recommended ;  and  was  disposed  on  this 
account  to  think  the  whole  of  their  study  narrow  and  shal- 
low. "Upon  this,"  says  Go  the,  "I  expounded  to  him, 
in  as  lively  a  way  as  I  could,  the  metamorphosis  of  plants, 
drawing  on  paper  for  him,  as  I  proceeded,  a  diagram  to 
represent  that  general  form  of  a  plant  which  shows  itself 
in  so  many  and  so  various  transformations.  Schiller  at- 
tended and  understood ;  and,  accepting  the  explanation, 
he  said,  '  This  is  not  observation,  but  an  idea.'  I  replied," 


OPPOSITION   OP   SENSATIONS   AND   IDEAS.  35 

adds  Gothe,  "with  some  degree  of  irritation;  for  the 
point  which  separated  us  was  most  luminously  marked  by 
this  expression:  but  I  smothered  my  vexation,  and 
merely  said,  '  I  was  happy  to  find  that  I  had  got  ideas 
without  knowing  it ;  nay,  that  I  saw  them  before  my 
eyes.' "  Gothe  then  goes  on  to  say,  that  he  had  been 
grieved  to  the  very  soul  by  maxims  promulgated  by 
Schiller,  that  no  observed  fact  ever  could  correspond  with 
an  idea ;  since  he  himself  loved  best  to  wander  in  the 
domain  of  external  observation,  he  had  been  led  to  look 
with  repugnance  and  hostility  upon  anything  which  pro- 
fessed to  depend  upon  ideas.  "Yet,"  he  observes,  "it 
occurred  to  me  that  if  my  observation  was  identical  with 
his  idea,  there  must  be  some  common  ground  on  which 
we  might  meet."  They  went  on  with  their  mutual  ex- 
planations, and  became  intimate  and  lasting  friends. 
"  And  thus,"  adds  the  poet,  "  by  means  of  that  mighty 
and  interminable  controversy  between  object  and  subject) 
we  two  concluded  an  alliance  which  remained  unbroken, 
and  produced  much  benefit  to  ourselves  and  others." 

The  general  diagram  of  a  plant,  of  which  Gothe  here 
speaks,  must  have  been  a  combination  of  lines  and  marks 
expressing  the  relations  of  position  and  equivalence  among 
the  elements  of  vegetable  forms,  -by  which  so  many  of 
their  resemblances  and  differences  may  be  explained. 
Such  a  symbol  is  not  an  Idea  in  that  general  sense  in 
which  we  propose  to  use  the  term,  but  is  a  particular 
modification  of  the  general  ideas  of  symmetry,  develope- 
ment,  and  the  like;  and  we  shall  hereafter  see,  according 
to  the  phraseology  which  we  shall  explain  in  the  next 
chapter,  such  a  diagram  might  express  the  ideal  conception 
of  a  plant. 

4.  Other  modes  of  expressing  this  antithesis. — Besides 
this  antithesis  of  subjective  and  objective,  some  of  the 
more  recent  schools  of  German  metaphysics  have  ex- 

D  2 


36  OF   IDEAS    IN   GENERAL. 

pressed  the  same  opposition  in  other  ways.  They 
have,  for  instance,  divided  the  universe  into  the  Me  and 
the  Not-me  (Ich  and  Nicht  Ic/i).  Upon  such  attempts,  we 
may  observe,  that  the  fundamental  distinction  between 
our  own  thoughts  and  the  objects  of  our  thoughts  is  of 
the  highest  consequence;  but  that,  if  this  distinction  be 
clearly  understood  and  recognised,  little  appears  to  be 
gained  by  expressing  it  in  any  novel  manner.  The  most 
weighty  part  of  the  philosopher's  task  is  to  analyse  the 
operations  of  the  mind,  and  for  this  purpose,  it  can  aid  us 
but  little  to  call  it,  instead  of  the  mind,  the  subject,  or  the 
me.  Whenever  it  appears  that  our  views  can  be  enun- 
ciated more  clearly  by  the  use  of  such  phraseology,  we 
shall  not  scruple  to  avail  ourselves  of  it;  but  we  shall  not 
think  it  necessary  to  dilate  upon  these  different  modes  of 
expressing  the  same  truth. 


CHAPTER  V. 
OF  IDEAL  CONCEPTIONS. 

1.  BY  what  has  been  said,  we  are  directed  towards  an 
analysis  of  our  thoughts  and  our  knowledge  into  two 
opposite  elements — Sensations,  and  Ideas.  The  latter  ele- 
ment will  require  further  examination ;  and  this  must  be 
the  more  carefully  conducted,  in  consequence  of  the  great 
vagueness  and  vacillation  with  which  the  term  has  com- 
monly been  used.  The  word  idea  is  not  unfrequently 
employed  to  designate  those  conceptions  which  the  mind 
forms,  and  which  it  expresses  by  means  of  general  terms ; 
for  example  (taking,  as  our  plan  requires,  instances 
from  the  sciences),  an  angle,  a  circle,  a  central  force,  a 
reflected  or  refracted  ray,  a  neutral  salt,  a  rose,  a  reptile. 
Or,  again,  we  may  employ  this  term  idea  to  express  cer- 


OF   IDEAL   CONCEPTIONS.  37 

tain  wider  fields  of  mental  apprehension,  each  of  which 
includes  many  such  conceptions  as  the  above;  as  when 
we  speak  of  the  idea  of  space,  of  time,  of  number,  of 
cause,  of  composition,  of  resemblance,  of  symmetry,  of 
organization.  It  will  be  necessary  for  our  purpose  to  dis- 
tinguish these  two  modes  of  thought.  The  latter  I  shall 
term  Fundamental  Ideas ;  and  I  shall,  in  the  succeeding 
Books,  enumerate  and  scrutinize  such  ideas  in  succession. 
The  other  class  of  notions  I  shall  term  Ideal  Conceptions, 
for  reasons  which  I  shall  soon  state. 

Each  of  the  Fundamental  Ideas  supplies  us  with  many 
Ideal  Conceptions.  Thus  straight  lines,  angles,  polygons, 
cubes,  tangents,  curvatures,  and  the  like,  are  all  modifi- 
cations of  the  fundamental  idea  of  space.  In  like  manner, 
the  fundamental  idea  of  cause  furnishes  us  with  such  con- 
ceptions as  accelerating  and  moving  force,  pressure  and 
inertia,  attraction  and  repulsion.  The  fundamental  idea 
of  resemblance  gives  rise  to  the  conceptions  of  class,  genus, 
species;  and  when  followed  into  futher  detail,  and  deve- 
loped by  the  suggestions  of  observation,  this,  along  with 
other  ideas,  produces  the  conception  of  a  particular  genus 
or  species,  as  a  rose ;  and  so  on,  in  other  cases. 

2.  Much  perplexity  and  difference  of  opinion  have  pre- 
vailed among  metaphysicians  respecting  these  ideal  con- 
ceptions. It  has  been  a  matter  of  long  and  intricate 
discussion,  what  is  the  object,  or  act,  of  thought,  which  is 
denoted  by  general  terms.  Some  have  held  that  we  have 
in  our  minds  a  real  idea,  something  of  the  nature  of  an 
image,  which  we  signify  by  such  terms ; — that  we  have,  in 
this  sense,  a  general  idea  of  an  angle,  a  polygon,  a  central 
force,  a  crystal,  a  rose.  Others  have  held  that  in  using 
such  terms  there  is  merely  an  act  of  the  mind  marked  by 
a  name; — an  act  by  which  the  mind  collects  and  connects 
many  impressions.  These  two  views  (that  of  thejRealists 
and  that  of  the  Nominalists)  have  prevailed,  with  various 


38  OF   IDEAS   IN   GENERAL. 

fluctuations  and  modifications,  through  all  ages  of  philo- 
sophy. But  that  either  opinion,  in  its  extreme  form, 
involves  us  in  insuperable  difficulties,  is  easily  seen :  and 
of  late,  both  parties  appear  to  be  willing  to  adopt  the 
word  conception  as  expressing  that  which  by  such  terms 
we  intend.  This  word,  indicating  both  an  act  of  the 
mind  by  which  unity  is  given  to  that  which  was  previously 
scattered,  and  the  result  of  the  act  abiding  with  us  when 
the  act  is  performed,  partakes  of  both  views,  so  far  as 
each  is  true,  and  will  most  conveniently  aid  us  in  pro- 
ceeding with  our  analysis. 

3.  But  to  the  word  Conception  I  join  the  adjective 
Ideal.  For  we  have  to  use  the  term,  not  to  describe  the 
mental  images  of  individual  objects  casually  taken,  but 
to  denote  those  definite  abstract  conceptions  which  are 
the  subjects  of  our  general  knowledge.  These  we  can 
reason  upon  securely,  precisely  because  they  are  modi- 
fications of  our  Fundamental  Ideas ;  for  these  Ideas,  as  we 
shall  hereafter  show,  contain  the  grounds  of  demonstra- 
tive truth.  The  Conception  of  a  Circle  is  determined 
by  relations  involved  in  the  Idea  of  space,  and  hence  its 
properties  can  be  certainly  known.  The  Conception  of 
mutual  attraction  involves  necessary  principles  derived 
from  theldea  of  cause.  The  Conception  of  a  crystalline 
arrangement  of  particles  involves  the  Idea  of  symmetry ; 
and  the  case  is  similar  in  other  examples.  Hence  I  term 
these  Ideal  Conceptions ;  intending  by  this  designation  to 
remind  the  reader  that  the  unity  which  these  conceptions 
give  to  the  circumstances  included  in  them,  is  not  a  casual 
or  arbitrary  unity,  but  is  derived  from  the  necessity  of 
the  case.  There  are  ideal  relations  which  necessarily 
form  the  foundation  of  our  knowledge  in  each  province 
of  human  thought ;  and  these  relations  govern  our  con- 
ceptions at  first,  as  well  as  determine  the  scientific  truths 
which,  by  means  of  our  conceptions  once  formed,  we  are 
able  to  enunciate. 


OF   IDEAL   CONCEPTIONS.  39 

4.  Since  the  Ideal  Conceptions,  of  which  we  here  speak, 
are  only  modifications  and  limitations  of  the  Fundamental 
Ideas  themselves,  the  reader  will  not  think  it  strange 
that  sometimes  it  may  not  be  easy  to  draw  a  line  of 
distinction  between  Ideas  and  Conceptions,  in  the  senses 
in   which  we  have  used  the   terms.     The  modification 
may  be  of  so   comprehensive  a  character  that  it  may 
appear  almost  as  extensive  as  the  idea  itself,  and  as  well 
fitted  to  supply  a  foundation  for  general  truths.  Thus,  we 
may  doubt  whether  Number  be  a  modification  of  the  Idea 
of  Time,  or  an  independent  Idea ;  and  some  persons  may 
decide  that  the  Idea  of  Number  supplies  us  with  principles 
which  are  the   proper  foundation  of  arithmetic,  without 
any  reference  to  the  Idea  of  Time.  In  like  manner,  some 
may  be  of  opinion  that   mechanical  Force  is  a  distinct 
Idea,  distinguishable  from  the  Idea  of  Cause,  and  capable 
of  affording  us  those  axioms  on  which  the  reasonings  of 
the  science  of  mechanics  must  rest.     Now,  with  respect 
to  doubts  and  ambiguities  of  this  kind,  we  may  observe, 
that  it  is  of  small  moment  to  our  view  of  the  Philosophy 
of  Science  how  they  are  decided.      Whether  Number 
and  Force  be  called  Ideas  or  Conceptions,  they  are  funda- 
mental so  far  as  the  sciences  founded  upon  them  are 
concerned;    and  they  partake   of   the   nature   of   ideas 
at   least   so   far   as   this,   that   they  are  the  sources  of 
necessary  truth,  as  we  shall  hereafter  show.     We  shall 
analyse  the  truths  of  arithmetic  and  of  mechanics,   so 
as  to  see  that  they  depend  upon   our  necessary  mode 
of  apprehending  number  and  force.     Whether  we  can 
analyse   these  modes   of  apprehension   still   further,   is 
another  question ; — not  without  interest  in  itself,  but  not 
affecting  our  previous  analysis.     Hence  it  will  not  be 
inconsistent  with  the  general  course  of  our  speculations, 
if  number,  force,  and  the  like  very  general  modifications 
of  our  ideas,   should  occasionally,   in   these   pages,   be 


40  OF    IDEAS    IN    GENERAL. 

themselves  termed  Ideas.  To  reduce  our  Fundamental 
Ideas  to  the  smallest  possible  number,  rigorously  inde- 
pendent of  each  other,  is  a  problem  which,  perhaps,  we 
have  not  completely  solved  in  the  present  work ;  but  any 
defect  in  the  solution  of  this  problem  will  by  no  means 
affect  our  general  reasonings. 

5.  It  has  been  said  by  some  writers*,  that  all  concep- 
tions, whether  ideal,  (that  is,  of  such  a  general  kind  as 
those  just  adduced,)  or  conceptions  of  particular  objects, 
are  merely  states  or  feelings  of  the  mind.  That  these 
conceptions  all  belong  to  the  mind  in  some  way,  being 
its  creations  or  acts,  or,  if  any  one  prefers  the  expres- 
sion, its  states  or  feelings,  (although  the  latter  terms  appear 
far  less  appropriate,)  it  is  superfluous  to  assert  or  to  deny. 
But  if  it  be  meant,  by  saying  that  all  conceptions  are 
merely  feelings  of  the  mind,  to  imply  that  this  general 
description  of  them  supersedes  or  diminishes  the  neces- 
sity of  examining  minutely  their  differences,  their  pro- 
perties, and  the  very  curious  and  complex  principles 
which  they  involve,  the  opinion  appears  to  be  very 
unphilosophical ;  and  the  phrase  which  suggests  it  is 
likely  only  to  mislead  us.  We  shall,  we  trust,  show 
hereafter,  that  these  acts  or  states  of  mind,  by  whatever 
name  they  be  called,  contain  in  them  very  fertile  and 
varied  elements  of  truth :  and  we  are  in  no  way  for- 
warded in  our  pursuit  of  such  elements,  by  being  told 
that  all  conceptions  about  which  we  can  reason  are 
merely  so  many  states  of  the  mind.  The  question  still 
remains,  what  are  the  peculiarities  of  each  of  those 
states?  and  to  what  conclusions  do  they  entitle  us  to 
proceed?  When  we  say  that  the  conceptions  of  straight 
lines  and  circles  are  merely  states  of  the  mind,  we  rather 
increase,  than  diminish,  the  difficulty  of  understanding 

*  BKOWN'SJ  Lectures,  vol.  ii. 


OF    IDEAL    CONCEPTIONS.  41 

how  these  states  of  mind,  and  no  other,  make  the  whole 
body  of  geometrical  knowledge  possible. 

We  must  now  endeavour  to  explain  in  what  manner 
such  Ideal  Conceptions  as  those  which  we  have  pointed 
out,  enter  into  the  formation  of  our  Knowledge. 


CHAPTER  VI. 
OF    INDUCTION. 

1 .  WHEN  we  have  become  possessed  of  such  ideal  con- 
ceptions as  those  just  described,  cases  frequently  occur 
in  which  we  can,  by  means  of  such  conceptions,  connect 
the  facts  which  we  learn  from  our  senses,  and  thus 
obtain  truths  from  materials  supplied  by  experience.  In 
such  cases,  the  truth  to  which  we  are  thus  led  is  said 
to  be  collected  from  the  observed  facts,  by  Induction. 

Thus  Hipparchus,  tracing  the  unequal  motion  of  the 
sun  among  the  stars,  in  different  parts  of  the  year,  as 
learnt  from  observation,  found  that  this  inequality 
might  be  fitly  represented  by  the  conception  of  an 
eccentric; — a  circle  in  which  the  sun  had  an  equable 
annual  motion,  the  spectator  not  being  situated  in  the 
centre  of  the  circle.  And  thus  he  established,  by  Induc- 
tion, the  truth  that  the  sun  appears  to  move  in  such  an 
eccentric.  At  a  later  period,  Kepler,  proceeding  upon 
more  exact  observations,  was  able  to  show  that,  not  a 
circle  about  an  eccentric  point,  but  an  ellipse  about  the 
focus,  was  the  conception  which  truly  agreed  with  the 
motion  of  the  earth,  and  of  the  other  planets,  about  the 
sun.  And  thus  the  elliptical  form  of  these  orbits  was 
established  by  Induction  from  many  observed  facts. 
Again,  to  take  an  example  of  another  kind,  the  forms  of 
flowers  may  have  applied  to  them  conceptions  borrowed 


42  OF   IDEAS  IN   GENERAL. 

from  the  idea  of  symmetry  of  parts ;  and  this  symmetry 
may  contain  three  similar  portions,  as  in  the  lily  and  its 
tribe;  or  five,  as  in  the  wild  rose,  and  many  others. 
Now,  it  appears  by  observation  of  many  particular  cases, 
that  these  differences  in  the  kind  of  symmetry  of  the 
flower  are  conjoined  with  differences  in  the  seed :  the 
tripartite  symmetry  prevailing  in  those  seeds  which  have 
only  one  cotyledon,  or  lobe  enveloping  the  embryo  ;  and 
the  quinquepartite  symmetry  in  those  seeds  which  have 
two  cotyledons.  Here,  then,  we  have  a  truth  concerning 
the  laws  of  vegetable  form,  established  by  Induction*. 

In  these,  and  in  all  cases  of  induction,  the  ideal  con- 
ception which  the  mind  itself  supplies  is  superinduced 
upon  the  facts  as  they  are  originally  presented  to  obser- 
vation. Before  the  inductive  truth  is  detected,  the  facts 
are  there,  but  they  are  many  and  unconnected.  The 
conception  which  the  discoverer  applies  to  them  gives 
them  connexion  and  unity.  Before  Hipparchus,  it  was 
known  that  the  motion  of  the  sun  was  not  equable ;  but 
it  appeared  to  be  irregular  and  lawless :  all  parts  of  the 
motion  became  regular  and  orderly,  by  the  introduction 
of  the  conception  of  the  eccentric.  In  the  case  of  Hip- 
parchus, we  can  only  conjecture  the  nature  of  the  efforts 
by  which  the  conception  was  discovered  and  applied 
to  the  facts.  But  in  Kepler's  case  we  know  from  his 
own  narrative  how  hard  lie  struggled  and  laboured  to 
find  the  right  conception ;  how  many  conceptions  he  tried 
and  rejected;  what  corrections  and  adjustments  of  his 
first  guesses  he  afterwards  introduced.  In  his  case  we 
see  in  the  most  conspicuous  manner  the  philosopher 
impressing  his  own  ideal  conception  upon  the  facts ;  the 
facts  being  exactly  fitted  to  this  conception,  although  no 
one  before  had  detected  such  a  fitness.  And  in  like 
manner,  in  all  other  cases,  the  discovery  of  a  truth  by 
*  Hist.  Inductive  Sciences,  iii.  338. 


OF   INDUCTION.  43 

induction  consists  in  finding  a  conception  or  combination 
of  conceptions  which  agrees  with,  connects,  and  arranges 
the  facts. 

2.  Such  ideal  conceptions  or  combinations  of  concep- 
tions, superinduced  upon  the  facts,  and  reducing  them  to 
rule  and  order,  are  theories.  And  thus  we  seem  to  have 
again  brought  before  us,  as  a  real  and  positive  distinc- 
tion, that  separation  of  fact  and  theory,  which,  in  the 
outset  of  our  inquiry  (Chap.  II.),  we  found  ourselves  com- 
pelled to  reject.  For  we  are  at  present  led  to  this 
result : — that  a  theory  is  a  truth  collected  from  facts  by 
induction ;  that  is,  by  superinducing  upon  the  facts  ideal 
conceptions  such  as  they  truly  agree  with. 

Of  the  apparent  contradiction  thus  brought  before 
us,  the  explanation  is  this : — that  what  we  commonly 
term  facts  involve  an  act  of  the  mind  of  the  same 
kind  as  that  which  we  have  described  as  induction, 
and  thus  do  not  in  that  respect  differ  essentially  from 
theory.  Thus  we  speak  of  the  eccentric  theory  of  the 
sun's  motions,  as  collected  by  induction  from  the  facts  of 
his  unequal  motion  at  different  times  of  the  year.  But 
these  facts  are  themselves  theories  collected  by  induction. 
For  they  depend  upon  the  conception  of  an  ecliptic,  or 
circle  passing  round  the  heavens,  in  which  ecliptic  the  sun's 
motion  at  each  time  is  to  be  inferred  by  referring  his 
places  to  the  stars.  But  this  ecliptic  and  these  modes  of 
reference  are  manifestly  creations  of  the  mind*  And 
notwithstanding  this  artificial  mode  of  measuring  the 
sun's  motion,  the  motion  itself  is  as  much  a  fact  as  the 
moon's  motion  among  the  stars,  which  is  visible  to  the 
eye.  Nor  is  there  essentially  any  difference  even  in  the 
mode  of  perceiving  these  motions.  For  in  our  apprehen- 
sion of  the  moon's  motion  among  the  stars,  we  assign  to 
her  a  path  and  a  velocity  which  are  conceptions  of  our 
own  minds,  and  no  mere  impressions  upon  the  senses. 
And  thus  as  theories  are  collected  by  induction  from  facts, 


44  OF   IDEAS   IN    GENERAL. 

facts  are  collected  by  an  induction  of  the  same  kind  from 
other  facts,  and  so  on,  till  we  approach  to  bare  impressions 
upon  the  senses,  which  yet  wre  can  never  quite  divest  of 
some  conception  or  other.  The  act  of  the  mind,  by 
which  it  converts  facts  into  theories,  is  of  the  same  kind 
as  that  by  which  it  converts  impressions  into  facts.  In 
both  cases  there  is  a  new  principle  of  unity  introduced 
by  the  mind,  an  ideal  connexion  established :  that  which 
was  many  becomes  one ;  that  which  was  loose  and  law- 
less becomes  connected  and  fixed  by  rule.  And  this  is 
done  by  induction ;  or,  as  we  have  described  this  process, 
by  superinducing  upon  the  facts,  as  given  by  observation, 
the  conception  of  our  own  minds. 

3.  It  has  already  been  noticed  that  there  is  in  different 
cases  a  wide  difference  as  to  the  degree  in  which  we  are 
conscious  of  this  operation.  In  some  cases  we  see  the 
facts  distinct  and  separate,  before  they  are  brought  to- 
gether by  the  conception  of  our  own  minds.  In  other 
cases  we  never  contemplate  them  thus  detached,  and 
can  hardly  conceive  them  under  any  other  form  than  that 
which  our  conceptions  give  them.  Yet  it  is  easy  to  see 
that  these  two  classes  of  cases  pass  into  each  other  by  in- 
sensible gradations.  To  take  an  example  of  this :  if  we 
had  to  decipher  an  ancient  inscription,  of  which  a  few 
broken  letters  and  imperfect  marks  only  remained,  we 
might  possibly,  by  an  intimate  acquaintance  with  the  lan- 
guage in  which  it  was  written,  and  with  the  usual  forms 
of  such  inscriptions,  and  by  the  aid  of  great  sagacity  and 
perseverance,  discover  the  meaning,  so  that  no  doubt 
should  remain  of  the  justness  of  our  conjecture.  In  this 
case,  we  might  with  propriety  assert  the  import  of  the 
legend  to  be  obtained  by  induction  from  the  few  facts 
which  were  placed  before  us.  If  the  inscription  were 
entire  and  plainly  legible,  we  should,  without  hesitation, 
assert  it  to  be  a  fact  that  we  had  before  cur  eyes  the 
declaration,  whatever  it  was,  which  the  legend  might  con- 


OF    INDUCTION.  45 

tain.  Yet  in  the  latter  case,  as  well  as  in  the  former,  it  is 
plain  that  there  is  much  which  the  mind  itself  supplies,  in 
addition  to  the  impressions  which  it  receives ;  much  which 
it  brings,  as  well  as  that  which  it  finds.  In  the  one  case, 
as  in  the  other,  the  reader  must  be  provided  with  know- 
ledge of  the  letters  and  of  the  language ;  and,  if  not  in 
the  same  degree  as  in  the  other  case,  yet  no  less  neces- 
sarily, with  attention  and  coherence  of  thought.  If  there 
be  induction  in  the  one  case,  it  must  exist,  more  obscurely, 
perhaps,  but  no  less  certainly,  in  the  other  also. 

And  thus  it  appears  that,  understanding  the  term 
induction  in  that  comprehensive  sense  in  which  alone  it 
is  consistent  with  itself,  it  is  requisite  to  give  unity  to  a 
fact,  no  less  than  to  give  connexion  to  a  theory ;  and  the 
conclusion  at  which  we  formerly  arrived,  that  fact  ana 
theory  pass  into  each  other  by  insensible  degrees,  is  not 
disturbed,  but  confirmed  and  illustrated  by  our  view  of 
induction,  as  the  act  of  superinducing  upon  the  impres- 
sions of  observation  an  ideal  conception,  by  which  they 
receive  connexion  and  unity. 


CHAPTER  VII. 
OF    SUCCESSIVE    GENERALIZATIONS. 

1.  THUS  we  are  again  led  to  the  doctrine,  that  Fact  and 
Theory  have  no  essential  difference,  except  in  the  degree 
of  their  certainty  and  familiarity.  Theory,  when  it 
becomes  firmly  established  and  steadily  lodged  in  the 
mind,  becomes  Fact ;  and  thus,  as  our  knowledge  becomes 
more  sure  and  more  extensive,  we  are  constantly  trans- 
ferring to  the  class  of  facts,  opinions  which  were  at  first 
regarded  as  theories. 

Now  we  have,  further  to  remark,  that  in  the  progress 


46  OF   IDEAS   IN   GENERAL. 

of  human  knowledge  respecting  any  branch  of  speculation, 
there  may  be  several  such  steps  in  succession,  each 
depending  upon  and  including  the  preceding.  The 
theoretical  views  which  one  generation  of  discoverers 
establishes,  become  the  facts  from  which  the  next  gene- 
ration advances  to  new  theories.  As  they  rise  from  the 
particular  to  the  general,  they  rise  from  what  is  general 
to  what  is  more  general.  Each  induction  supplies  the 
materials  of  fresh  inductions ;  each  generalization,  with 
all  that  it  embraces  in  its  circle,  may  be  found  to  be  but 
one  of  many  circles,  comprehended  within  the  circuit  of 
some  wider  generalization. 

This  remark  has  already  been  made,  and  illustrated, 
in  the  History  of  the  Inductive  Sciences*;  and,  in  truth, 
the  whole  of  the  history  of  science  is  full  of  suggestions 
and  exemplifications  of  this  course  of  things.  It  may  be 
convenient,  however,  to  select  a  few  instances  which  may 
further  explain  and  confirm  this  view  of  the  progress  of 
scientific  knowledge. 

2.  The  most  conspicuous  instance  of  this  succession  is 
to  be  found  in  that  science  which  has  been  progressive  from 
the  beginning  of  the  world  to  our  own  times,  and  which 
exhibits  by  far  the  richest  collection  of  successive  disco- 
veries :  I  mean  astronomy.  It  is  easy  to  see  that  each  of 
these  successive  discoveries  depended  on  those  antece- 
dently made,  and  that  in  each,  the  truths  which  were  the 
highest  point  of  the  knowledge  of  one  age  were  the  fun- 
damental basis  of  the  efforts  of  the  age  which  came  next. 
Thus  we  find,  in  the  days  of  Greek  discovery,  Hipparchus 
and  Ptolemy  combining  and  explaining  the  particular 
facts  of  the  motion  of  the  sun,  moon,  and  planets,  by 
means  of  the  theory  of  epicycles  and  eccentrics  ; — a  highly 
important  step,  which  gave  an  intelligible  connexion  and 
rule  to  the  motions  of  each  of  these  luminaries.  When 

*  Hist.  Inductive  Sciences,  ii.  182. 


OF   SUCCESSIVE   GENERALIZATIONS.  47 

these  cycles  and  epicycles,  thus  truly  representing  the 
apparent  motions  of  the  heavenly  bodies,  had  accumulated 
to  an  inconvenient  amount,  by  the  discovery  of  many 
inequalities  in  the  observed  motions,  Copernicus  showed 
that  their  effects  might  all  be  more  simply  included,  by 
making  the  sun  the  centre  of  motion  of  the  planets,  in- 
stead of  the  earth.  But  in  this  new  view  he  still  retained 
the  epicycles  and  eccentrics  which  governed  the  motion 
of  each  body.  Tycho  Brahe's  observations,  and  Kepler's 
calculations,  showed  that,  besides  the  vast  number  of  facts 
which  the  epicyclical  theory  could  account  for,  there  were 
some  which  it  would  not  exactly  include,  and  Kepler  was 
led  to  the  persuasion  that  the  planets  move  in  ellipses. 
But  this  view  of  motion  was  at  first  conceived  by  Kepler 
as  a  modification  of  the  conception  of  epicycles.  On  one 
occasion  he  blames  himself  for  not  sooner  seeing  that  such 
a  modification  was  possible.  "  What  an  absurdity  on  my 
part !"  he  cries*;  "  as  if  libra tion  in  the  diameter  of  the 
epicycle  might  not  come  to  the  same  thing  as  motion  in 
the  ellipse."  But  again ;  Kepler's  laws  of  the  elliptical 
motion  of  the  planets  were  established ;  and  these  laws 
immediately  became  the  facts  on  which  the  mathema- 
ticians had  to  found  their  mechanical  theories.  From 
these  facts  Newton,  as  we  have  related,  proved  that  the 
central  force  of  the  sun  retains  the  planets  in  their  orbits, 
according  to  the  law  of  the  inverse  square  of  the  dis- 
tance. The  same  law  was  shown  to  prevail  in  the  gravi- 
tation of  the  earth.  It  was  shown,  too,  by  induction 
from  the  motions  of  Jupiter  and  Saturn,  that  the  planets 
attract  each  other ;  by  calculations  from  the  figure  of  the 
earth,  that  the  parts  of  the  earth  attract  each  other;  and, 
by  considering  the  course  of  the  tides,  that  the  sun  and 
moon  attract  the  waters  of  the  ocean.  And  all  these 
curious  discoveries  being  established  as  facts,  the  subject 
*  Hist.  Inductive  Sciences,  i.  428. 


48  OF    IDEAS    IN    GENERAL. 

was  ready  for  another  step  of  generalization.  By  an  un- 
paralleled rapidity  in  the  progress  of  discovery  in  this 
case,  not  only  were  all  the  inductions  which  we  have  first 
mentioned  made  by  one  individual,  but  the  new  advance, 
the  higher  flight,  the  closing  victory,  fell  to  the  lot  of  the 
same  extraordinary  person. 

The  attraction  of  the  sun  upon  the  planets,  of  the 
moon  upon  the  earth,  of  the  planets  on  each  other,  of  the 
parts  of  the  earth  on  themselves,  of  the  sun  and  moon 
upon  the  ocean  ; — all  these  truths,  each  of  itself  a  great 
discovery,  were  included  by  Newton  in  the  higher  gene- 
ralization, of  the  universal  gravitation  of  matter,  by  which 
each  particle  is  drawn  to  each  other  according  to  the  law 
of  the  inverse  square :  and  thus  this  long  advance  from 
discovery  to  discovery,  from  truths  to  truths,  each  justly 
admired  when  new,  and  then  rightly  used  as  old,  was 
closed  in  a  worthy  and  consistent  manner,  by  a  truth 
which  is  the  most  worthy  admiration,  because  it  includes 
all  the  researches  of  preceding  ages  of  astronomy. 

3.  We  may  take  another  example  of  a  succession  of 
this  kind  from  the  history  of  a  science,  which,  though  it 
has  made  wonderful  advances,  has  not  yet  reached  its  goal, 
as  physical  astronomy  appears  to  have  done,  but  seems  to 
have  before  it  a  long  prospect  of  future  progress.  I  now 
refer  to  chemistry,  in  which  I  shall  try  to  point  out  how 
the  preceding  discoveries  afforded  the  materials  of  the 
succeeding;  although  this  subordination  and  connexion 
is,  in  this  case,  less  familiar  to  men's  minds  than  in  astro- 
nomy, and  is,  perhaps,  more  difficult  to  present  in  a  clear 
and  definite  shape.  Sylvius  saw,  in  the  facts  which 
occur,  when  an  acid  and  an  alkali  are  brought  together, 
the  evidence  that  they  neutralize  each  other.  But  cases 
of  neutralization,  and  acidification,  and  many  other  effects 
of  mixture  of  the  ingredients  of  bodies,  being  thus  viewed 
as  facts,  had  an  aspect  of  unity  and  law  given  them  by 


OF   SUCCESSIVE   GENERALIZATIONS.  49 

Geoffroy  and  Bergman*,  who  introduced  the  conception 
of  the  chemical  affinity  or  elective  attraction,  by  which 
certain  elements  select  other  elements,  as  if  by  preference. 
That  combustion,  whether  a  chemical  union  or  a  chemi- 
cal separation  of  ingredients,  is  of  the  same  nature  with 
acidification,  was  the  doctrine  of  Beccher  and  Stahl,  and 
was  soon  established  as  a  truth  which  must  form  a  part 
of  every  succeeding  physical  theory.  That  the  rules  of 
affinity  and  chemical  composition  may  include  gaseous 
elements,  was  established  by  Black  and  Cavendish.  And 
all  these  truths,  thus  brought  to  light  by  chemical  disco- 
verers,— affinity,  the  identity  of  acidification  and  combus- 
tion, the  importance  of  gaseous  elements, — along  with  all 
the  facts  respecting  the  weight  of  ingredients  and  com- 
pounds which  the  balance  disclosed, — were  taken  up, 
connected,  and  included  as  particulars  in  the  oxygen 
theory  of  Lavoisier.  Again,  the  results  of  this  theory,  and 
the  quantity  of  the  several  ingredients  which  entered 
into  each  compound — (such  results,  for  the  most  part, 
being  now  no  longer  mere  theoretical  speculations,  but 
recognised  facts) — were  the  particulars  from  which  Dalton 
derived  that  wide  law  of  chemical  combination  which  we 
term  the  atomic  theory.  And  this  law,  soon  generally 
accepted  among  chemists,  is  already  in  its  turn  become 
one  of  t\\Q  facts  included  in  Faraday's  theory  of  the  identity 
of  chemical  affinity  and  electric  attraction. 

It  is  unnecessary  to  give  further  exemplifications  of 
this  constant  ascent  from  one  step  to  a  higher ; — this  per- 
petual conversion  of  true  theories  into  the  materials  of 
other  and  wider  theories.  It  will  hereafter  be  our  busi- 
ness to  exhibit,  in  a  more  full  and  formal  manner,  the 
mode  in  which  this  principle  determines  the  whole  scheme 
and  structure  of  all  the  most  exact  sciences.  And  thus, 
beginning  with  the  facts  of  sense,  we  gradually  climb  to 

*  Hist.  Inductive  Sciences,  iii.  112. 
VOL.  I.  E 


50  OF    IDEAS    IN    GENERAL. 

the  highest  forms  of  human  knowledge,  and  obtain  from 
experience  and  observation  a  vast  collection  of  the  most 
wide  and  elevated  truths. 

There  are,  however,  truths  of  a  very  different  kind,  to 
which  we  must  turn  our  attention,  in  order  to  pursue  our 
researches  respecting  the  nature  and  grounds  of  our 
knowledge.  But  before  we  do  this,  we  must  notice  one 
more  feature  in  that  progress  of  science  which  we  have 
already  in  part  described. 


CHAPTER  VIII. 
OF    TECHNICAL    TERMS. 

1.  IT  has  already  been  stated  that  we  gather  know- 
ledge from  the  external  world,  when  we  are  able  to  apply, 
to  the  facts  which  we  observe,  some  ideal  conception, 
which  gives  unity  and  connexion  to  multiplied  and 
separate  perceptions.  We  have  also  shown  that  our 
conceptions,  thus  verified  by  facts,  may  themselves  be 
united  and  connected  by  a  new  bond  of  the  same  nature ; 
and  that  man  may  thus  have  to  pursue  his  way  from 
truth  to  truth  through  a  long  progression  of  discoveries, 
each  resting  on  the  preceding,  and  rising  above  it. 

It  is  now  further  to  be  noticed  that  each  of  these 
steps,  in  succession,  is  recorded,  fixed,  and  made  available, 
by  some  peculiar  form  of  words ;  and  such  words,  thus 
rendered  precise  in  their  meaning,  and  appropriated  to 
the  service  of  science,  we  may  call  Technical  Terms.  It 
is  in  a  great  measure  by  inventing  such  Terms  that  men 
not  only  best  express  the  discoveries  they  have  made? 
but  also  enable  their  followers  to  become  so  familiar 
with  these  discoveries,  and  to  possess  them  so  thoroughly, 
that  they  can  readily  use  them  in  advancing  to  ulterior 
generalizations. 


OF   TECHNICAL   TERMS.  51 

Most  of  our  ideal  conceptions  are  described  by  exact 
and  constant  words  or  phrases,  such  as  those  of  which  we 
here  speak.  We  have  already  had  occasion  to  employ 
many  of  these.  Thus  we  have  had  instances  of  technical 
terms  expressing  geometrical  conceptions,  as  ellipsis, 
radius  vector,  axis,  plane,  the  proportion  of  the  inverse 
square,  and  the  like.  Other  terms  have  described  mecha- 
nical conceptions,  as  accelerating  force  and  attraction. 
Again,  chemistry  exhibits  (as  do  all  sciences)  a  series  of 
terms  which  mark  the  steps  of  her  progress.  The  views 
of  the  first  real  founders  of  the  science  are  recorded  by 
the  terms  which  are  still  in  use,  neutral  salts,  affinity,  and 
the  like.  The  establishment  of  Dalton's  theory  has  pro- 
duced the  use  of  the  word  atom  in  a  peculiar  sense,  or 
of  some  other  word,  as  proportion,  in  a  sense  equally 
technical.  And  Mr.  Faraday  has  found  it  necessary,  in 
order  to  expound  his  electro-chemical  theory,  to  intro- 
duce such  terms  as  anode  and  cathode,  an'ion  and  cath'ion. 

2.  I  need  not  adduce  any  further  examples,  for  my 
object  at  present  is  only  to  point  out  the  use  and  influence 
of  such  language :  its  rules  and  principles  I  shall  hereafter 
try,  in  some  measure,  to  fix.  But  what  we  have  here  to 
remark  is,  the  extraordinary  degree  in  which  the  progress 
of  science  is  facilitated,  by  thus  investing  each  new  dis- 
covery with  a  compendious  and  steady  form  of  expression. 
These  terms  soon  become  part  of  the  current  language  of 
all  who  take  an  interest  in  speculation.  However  strange 
they  may  sound  at  first,  they  soon  grow  familiar  in  our 
ears,  and  are  used  without  any  effort  or  recollection  of  the 
difficulty  they  once  involved.  They  become  as  common 
as  the  phrases  which  express  our  most  frequent  feelings 
and  interests,  while  yet  they  have  incomparably  more 
precision  than  belongs  to  any  terms  which  express  feel- 
ings; and  they  carry  with  them,  in  their  import,  the  results 
of  deep  and  laborious  trains  of  research.  They  convey  the 

E  2 


52  OF   IDEAS   IN   GENERAL. 

mental  treasures  of  one  period  to  the  generations  that 
follow ;  and  laden  with  this,  their  precious  freight,  they  sail 
safely  across  gulfs  of  time  in  which  empires  have  suffered 
shipwreck,  and  the  languages  of  common  life  have  sunk 
into  oblivion.  We  have  still  in  constant  circulation 
among  us  the  terms  which  belong  to  the  geometry,  the 
astronomy,  the  zoology,  the  medicine  of  the  Greeks,  and 
the  algebra  and  chemistry  of  the  Arabians.  And  we  can 
in  an  instant,  by  means  of  a  few  words,  call  to  our  own 
recollection,  or  convey  to  the  apprehension  of  another 
person,  phenomena  and  relations  of  phenomena  in  optics, 
mineralogy,  chemistry,  which  are  so  complex  and  abstruse, 
that  it  might  seem  to  require  the  utmost  subtlety  of  the 
human  mind  to  grasp  them,  even  if  that  were  made  the 
sole  object  of  its  efforts.  By  this  remarkable  effect  of 
technical  language,  we  have  the  results  of  all  the  labours 
of  past  times  not  only  always  accessible,  but  so  prepared 
that  we  may  (provided  we  are  careful  in  the  use  of  our 
instrument)  employ  what  is  really  useful  and  efficacious 
for  the  purpose  of  further  success,  without  being  in  any 
way  impeded  or  perplexed  by  the  length  and  weight  of 
the  chain  of  past  connexions  which  we  drag  along 
with  us. 

By  such  means, — by  the  use  of  the  inductive  process, 
and  by  the  aid  of  technical  terms, — man  has  been  constantly 
advancing  in  the  path  of  scientific  truth.  In  a  succeed- 
ing part  of  this  work  we  shall  endeavour  to  trace  the 
general  rules  of  this  advance,  and  to  lay  down  the  maxims 
by  which  it  may  be  most  successfully  guided  and  for- 
warded. But  in  order  that  we  may  do  this  to  the  best 
advantage,  we  must  pursue  still  further  the  analysis  of 
knowledge  into  its  elements;  and  this  will  be  our  employ- 
ment in  the  first  part  of  the  work. 


CHAPTER  IX. 
OF  NECESSARY  AND  CONTINGENT  TRUTHS. 

1.  Course  of  the  Argument. — Every  advance  in  human 
knowledge  consists,  as  we  have  seen,  in  adapting 
new  ideal  conceptions  to  ascertained  facts,  and  thus 
in  superinducing  the  form  upon  the  matter,  the  active 
upon  the  passive  processes  of  our  minds.  Every  such 
step  introduces  into  our  knowledge  an  additional  portion 
of  the  ideal  element,  and  of  those  relations  which  flow 
from  the  nature  of  ideas.  It  is,  therefore,  important  for 
our  purpose  to  examine  more  closely  this  element,  and  to 
learn  what  the  relations  are  which  may  thus  come  to  form 
part  of  our  knowledge.  An  inquiry  into  those  ideas 
which  form  the  foundations  of  our  sciences; — into  the 
reality,  independence,  extent,  and  principal  heads  of  the 
knowledge  which  we  thus  acquire ; — is  a  task  on  which  we 
must  now  enter,  and  which  will  employ  us  for  several  of 
the  succeeding  Books. 

In  this  inquiry  our  object  will  be  to  pass  in  review  all 
the  most  important  fundamental  ideas  which  our  sciences 
involve ;  and  to  prove  more  distinctly  in  reference  to 
each,  what  we  have  already  asserted  with  regard  to 
all,  that  there  are  everywhere  involved  in  our  knowledge 
acts  of  the  mind  as  well  as  impressions  of  sense ;  and  that 
our  knowledge  derives,  from  these  acts,  a  generality,  cer- 
tainty, and  evidence  which  the  senses  could  in  no  degree 
have  supplied.  But  before  I  proceed  to  do  this  in  par- 
ticular cases,  I  will  give  some  account  of  the  argument 
in  its  general  form. 

We  have  already  considered  the  separation  of  our 
knowledge  into  its  two  elements, — Impressions  of  Sense 
and  Ideas, — as  evidently  indicated  by  this ;  that  all  know- 
ledge possesses  characters  which  neither  of  these  elements 


54  OF   IDEAS   IN   GENERAL. 

alone  could  bestow.  Without  our  ideas,  our  sensations 
could  have  no  connexion ;  without  external  impressions, 
our  ideas  would  have  no  reality ;  and  thus  both  ingredi- 
ents of  our  knowledge  must  exist.  But  there  is  another 
mode  in  which  we  may  prove  the  distinct  and  indepen- 
dent existence  of  these  two  elements,  namely,  by  con- 
sidering that  there  are  two  large  classes  of  truths  which 
differ  entirely  from  each  other,  and  of  which  the  differ- 
ence arises  from  this,  that  the  one  class  derives  its 
nature  from  the  one,  and  the  other  from  the  other,  of 
these  two  elements.  These  are  what  are  technically 
termed  necessary  and  contingent  truths ;  truths  of  demon- 
stration and  truths  of  experience.  I  shall  first  point  out 
the  difference  of  these  two  kinds  of  truths,  which  differ- 
ence is  briefly  this,  that  the  former  are  true  universally 
and  necessarily,  the  latter,  only  learnt  from  experience, 
and  limited  by  experience.  I  shall  show  that  upon  vari- 
ous subjects  we  possess  truths  of  the  former  kind ;  that 
the  universality  and  necessity  which  distinguish  them  can 
by  no  means  be  derived  from  experience ;  that  these  cha- 
racters do  in  reality  flow  from  the  ideas  which  these 
truths  involve ;  and  that  when  their  necessity  is  exhibited 
in  the  way  of  logical  demonstration,  it  is  found  to  depend 
upon  certain  fundamental  principles,  (Definitions  and 
Axioms,)  which  may  thus  be  considered  as  expressing, 
n  some  measure,  the  essential  characters  of  our  ideas. 
These  fundamental  principles  I  shall  afterwards  proceed  to 
discuss  and  to  exhibit  in  each  of  the  principal  depart- 
ments of  science. 

2.  Of  Necessary  Truths. — Necessary  truths  are  those 
in  which  we  not  only  learn  that  the  proposition  is 
true,  but  see  that  it  must  be  true ;  in  which  the  negation 
of  the  truth  is  not  only  false,  but  impossible ;  in  which 
we  cannot,  even  by  an  effort  of  imagination,  or  in  a  sup- 
position, conceive  the  reverse  of  that  which  is  asserted. 


OF   NECESSARY   AND   CONTINGENT   TRUTHS.  55 

That  there  are  such  truths  cannot  be  doubted.  We 
may  take,  for  example,  all  relations  of  number.  Three 
and  Two  added  together  make  Five.  We  cannot  con- 
ceive it  to  be  otherwise.  We  cannot,  by  any  freak  of 
thought,  imagine  Three  and  Two  to  make  Seven. 

It  may  be  said  that  this  assertion  merely  expresses 
what  we  mean  by  our  words ;  that  it  is  a  matter  of  defi- 
nition ;  that  the  proposition  is  an  identical  one. 

But  this  is  by  no  means  so.  The  definition  of  Five  is 
not  Three  and  Two,  but  Four  and  One.  How  does  it 
appear  that  Three  and  Two  is  the  same  number  as  Four 
and  One  ?  It  is  evident  that  it  is  so ;  but  why  is  it  evi- 
dent?— not  because  the  proposition  is  identical;  for  if 
that  were  the  reason,  all  numerical  propositions  must  be 
evident  for  the  same  reason.  If  it  be  a  matter  of  defi- 
nition that  3  and  2  make  5,  it  must  be  a  matter  of  defi- 
nition that  39  and  27  make  66.  But  who  will  say  that 
the  definition  of  66  is  39  and  27  ?  Yet  the  magnitude 
of  the  numbers  can  make  no  difference  in  the  ground  of 
the  truth.  How  do  we  know  that  the  product  of  13  and 
17  is  4  less  than  the  product  of  15  and  15  ?  We  see 
that  it  is  so,  if  we  perform  certain  operations  by  the  rules 
of  arithmetic ;  but  how  do  we  know  the  truth  of  the 
rules  of  arithmetic?  If  we  divide  123375  by  987 
according  to  the  process  taught  us  at  school,  how  are  we 
assured  that  the  result  is  correct,  and  that  the  number 
125  thus  obtained  is  really  the  number  of  times  one 
number  is  contained  in  the  other  ? 

The  correctness  of  the  rule,  it  may  be  replied,  can  be 
rigorously  demonstrated.  It  can  be  shown  that  the  pro- 
cess must  inevitably  give  the  true  quotient. 

Certainly  this  can  be  shown  to  be  the  case.  And 
precisely  because  it  can  be  shown  that  the  result  must  be 
true,  we  have  here  an  example  of  a  necessary  truth ;  and 
this  truth,  it  appears,  is  not  therefore  necessary  because  it 


56  OF   IDEAS   IN   GENERAL. 

is  itself  evidently  identical,  however  it  may  be  possible  to 
prove  it  by  reducing  it  to  evidently  identical  propositions. 
And  the  same  is  the  case  with  all  other  numerical  propo- 
sitions ;  for,  as  we  have  said,  the  nature  of  all  of  them  is 
the  same. 

Here,  then,  we  have  instances  of  truths  which  are  not 
only  true,  but  demonstrably  and  necessarily  tr  u  e.  Now  such 
truths  are,  in  this  respect  at  least,  altogether  different 
from  truths,  which,  however  certain  they  may  be,  are 
learnt  to  be  so  only  by  the  evidence  of  observation,  in- 
terpreted, as  observation  must  be  interpreted,  by  our  own 
mental  faculties.  There  is  no  difficulty  in  finding  ex- 
amples of  these  merely  observed  truths.  We  find  that 
sugar  dissolves  in  water,  and  forms  a  transparent  fluid, 
but  no  one  will  say  that  we  can  see  any  reason  beforehand 
why  the  result  must  be  so.  We  find  that  all  animals 
which  chew  the  cud  also  have  the  divided  hoof;  but  could 
any  one  have  predicted  that  this  would  be  universally  the 
case  ?  or  supposing  the  truth  of  the  rule  to  be  known,  can 
any  one  say  that  he  cannot  conceive  the  facts  as  occurring 
otherwise?  Water  expands  when  it  crystallizes,  some 
other  substances  contract  in  the  same  circumstances ;  but 
can  any  one  know  that  this  will  be  so  otherwise  than  by 
observation  ?  We  have  here  propositions  rigorously  true, 
(we  will  assume,)  but  can  any  one  say  they  are  necessarily 
true  ?  These,  and  the  great  mass  of  the  doctrines  esta- 
blished by  induction,  are  actual,  but  so  far  as  we  can  see, 
accidental  laws ;  results  determined  by  some  unknown  se- 
lection, not  demonstrable  consequences  of  the  essence  of 
things,  inevitable  and  perceived  to  be  inevitable.  According 
to  the  phraseology  which  has  been  frequently  used  by  phi- 
losophical writers,  they  are  contingent,  not  necessary  truths. 

It  is  requisite  to  insist  upon  this  opposition,  because 
no  insight  can  be  obtained  into  the  true  nature  of 
knowledge,  and  the  mode  of  arriving  at  it,  by  any  one 


OF    NECESSARY    AND    CONTINGENT   TRUTHS.  57 

who  does  not  clearly  appreciate  the  distinction.  The 
separation  of  truths  which  are  learnt  by  observation,  and 
truths  which  can  be  seen  to  be  true  by  a  pure  act  of 
thought,  is  one  of  the  first  and  most  essential  steps  in 
our  examination  of  the  nature  of  truth,  and  the  mode  of 
its  discovery.  If  any  one  does  not  clearly  comprehend 
this  distinction  of  necessary  and  contingent  truths,  he 
will  not  be  able  to  go  along  with  us  in  our  researches 
into  the  foundations  of  human  knowledge ;  nor,  indeed, 
to  pursue  with  success  any  speculation  on  the  subject. 
But,  in  fact,  this  distinction  is  one  that  can  hardly  fail 
to  be  at  once  understood.  It  is  insisted  upon  by  almost 
all  the  best  modern,  as  well  as  ancient,  metaphysicians*, 
as  of  primary  importance.  And  if  any  person  does  not 
fully  apprehend,  at  first,  the  different  kinds  of  truth  thus 
pointed  out,  let  him  study,  to  some  extent,  those  sciences 
which  have  necessary  truth  for  their  subject,  as  geometry, 
or  the  properties  of  numbers,  so  as  to  obtain  a  familiar 
acquaintance  with  such  truth ;  and  he  will  then  hardly 
fail  to  see  how  different  the  evidence  of  the  propositions 
which  occur  in  these  sciences,  is  from  the  evidence  of 
the  facts  which  are  merely  learnt  from  experience. 
That  the  year  goes  through  its  course  in  365  days,  can 
only  be  known  by  observation  of  the  sun  or  stars :  that 
365  days  is  52  weeks  and  a  day,  it  requires  no  expe- 
rience, but  only  a  little  thought  to  perceive.  That  bees 
build  their  cells  in  the  form  of  hexagons,  we  cannot 
know  without  looking  at  them ;  that  regular  hexagons 
may  be  arranged  so  as  to  fill  space,  may  be  proved  with 
the  utmost  rigour,  even  if  there  were  not  in  existence 
such  a  thing  as  a  material  hexagon. 

I  have  taken  examples  of  necessary  truths  from  the 
properties  of  number  and  space ;  but  such  truths  exist 
no  less  in  other  subjects,  although  the  discipline  of 

*  Aristotle,  Dr.  Whately,  Dugald  Stewart,  &c. 


58  OF   IDEAS   IN   GENERAL. 

thought  which  is  requisite  to  perceive  them  distinctly, 
may  not  be  so  usual  among  men  with  regard  to  the 
sciences  of  mechanics  and  hydrostatics,  as  it  is  with 
regard  to  the  sciences  of  geometry  and  arithmetic.  Yet 
every  one  may  perceive  that  there  are  such  truths  in 
mechanics.  If  I  press  the  table  with  my  hand,  the 
table  presses  my  hand  with  an  equal  force :  here  is  a 
self-evident  and  necessary  truth.  In  any  machine, 
constructed  in  whatever  manner  to  increase  the  force 
which  I  can  exert,  it  is  certain  that  what  I  gain  in  force 
I  must  lose  in  the  velocity  which  I  communicate.  This 
is  not  a  contingent  truth,  borrowed  from  and  limited  by 
observation ;  for  a  man  of  sound  mechanical  views  applies 
it  with  like  confidence,  however  novel  be  the  construc- 
tion of  the  machine.  When  I  come  to  speak  of  the  ideas 
which  are  involved  in  our  mechanical  knowledge,  I 
may,  perhaps,  be  able  to  bring  more  clearly  into  view 
the  necessary  truth  of  general  propositions  on  such 
subjects.  That  reaction  is  equal  and  opposite  to  action 
is  as  necessarily  true  as  that  two  straight  lines  cannot 
inclose  a  space ;  it  is  as  impossible  theoretically  to  make 
a  perpetual  motion  by  mere  mechanism  as  to  make  the 
diagonal  of  a  square  commensurable  with  the  side. 

The  existence  of  these  two  kinds  of  truth,  necessary 
and  contingent,  and  their  separate  nature,  being  estab- 
lished or  allowed,  we  proceed  onwards  with  the  argument. 

Necessary  truths  must  be  universal  truths.  If  any 
property  belong  to  a  right-angled  triangle  necessarily,  it 
must  belong  to  all  right-angled  triangles.  And  it  shall  be 
proved  in  the  following  Chapter,  that  truths  possessing 
these  two  characters,  of  Necessity  and  Universality,  can- 
not possibly  be  the  mere  results  of  experience. 


59 

CHAPTER  X. 
OF    EXPERIENCE. 

1.  I  HERE  employ  the  term  Experience  in  a  more 
definite  and  limited  sense  than  it  possesses  in  common 
usage ;  for  I  restrict  it  to  matters  belonging  to  the 
domain  of  science.  In  such  cases,  the  knowledge  which 
we  acquire,  by  means  of  experience,  is  of  a  clear  and 
precise  nature ;  and  the  passions  and  feelings  and 
interests,  which  make  the  lessons  of  experience  in  prac- 
tical matters  so  difficult  to  read  aright,  no  longer  disturb 
and  confuse  us.  We  may,  therefore,  hope,  by  attending 
to  such  cases,  to  learn  what  efficacy  experience  really 
has,  in  the  discovery  of  truth. 

That  from  experience  (including  intentional  expe- 
rience, or  observation,)  we  obtain  much  knowledge  which 
is  highly  important,  and  which  could  not  be  procured 
from  any  other  source,  is  abundantly  clear.  We  have 
already  taken  several  examples  of  such  kuowledge. 
We  know  by  experience  that  animals  which  ruminate 
are  cloven-hoofed ;  and  we  know  this  in  no  other 
manner.  We  know,  in  like  manner,  that  all  the 
planets  and  their  satellites  revolve  round  the  sun  from 
west  to  east.  It  has  been  found  by  experience  that  all 
meteoric  stones  contain  chrome.  Many  similar  portions 
of  our  knowledge  might  be  mentioned. 

Now  what  we  have  here  to  remark  is  this ; — that  in 
no  case  can  experience  prove  a  proposition  to  be  neces- 
sarily or  universally  true.  However  many  instances  we 
may  have  observed  of  the  truth  of  a  proposition,  yet  if  it 
be  merely  observation,  there  is  nothing  to  assure  us  that 
the  next  case  shall  not  be  an  exception  to  the  rule.  If 
it  be  strictly  true  that  every  ruminant  animal  yet  known 
has  cloven  hoofs,  we  still  cannot  be  sure  that  some 


60  OF   IDEAS   IN   GENERAL. 

creature  will  not  hereafter  be  discovered  which  has  the 
first  of  these  attributes  without  having  the  other. 
When  the  planets  and  their  satellites,  as  far  as  Saturn, 
had  been  all  found  to  move  round  the  sun  in  one  direc- 
tion, it  was  still  possible  that  there  might  be  other  such 
bodies  not  obeying  this  rule ;  and,  accordingly,  when  the 
satellites  of  Uranus  were  detected,  they  appeared  to 
offer  an  exception  of  this  kind.  Even  in  the  mathe- 
matical sciences,  we  have  examples  of  such  rules  sug- 
gested by  experience,  and  also  of  their  precariousness. 
However  far  they  may  have  been  tested,  we  cannot 
depend  upon  their  correctness,  except  we  see  some 
reason  for  the  rule.  For  instance,  various  rules  have 
been  given,  for  the  purpose  of  pointing  out  prime 
numbers ;  that  is,  those  which  cannot  be  divided  by  any 
other  number.  We  may  try,  as  an  example  of  such  a 
rule,  this  one — any  odd  power  of  the  number  two,  dimi- 
nished by  one.  Thus  the  third  power  of  two,  diminished 
by  one,  is  seven ;  the  fifth  power,  diminished  by  one,  is 
thirty-one;  the  seventh  power  so  diminished  is  one 
hundred  and  twenty-seven.  All  these  are  prime  num- 
bers :  and  we  might  be  led  to  suppose  that  the  rule  is 
universal.  But  the  next  example  shows  us  the  falla- 
ciousness of  such  a  belief.  The  ninth  power  of  two, 
diminished  by  one,  is  five  hundred  and  eleven,  which  is 
not  a  prime,  being  divisible  by  seven. 

Experience  must  always  consist  of  a  limited  nnmber 
of  observations.  And,  however  numerous  these  may  be, 
they  can  show  nothing  with  regard  to  the  infinite 
number  of  cases  in  which  the  experiment  has  not  been 
made.  Experience  being  thus  unable  to  prove  a  fact  to 
be  universal,  is,  as  will  readily  be  seen,  still  more 
incapable  of  proving  a  truth  to  be  necessary.  Expe- 
rience cannot,  indeed,  offer  the  smallest  ground  for  the 
necessity  of  a  proposition.  She  can  observe  and  record 


OF   EXPERIENCE.  61 

what  has  happened  ;  but  she  cannot  find,  in  any  case,  or 
in  any  accumulation  of  cases,  any  reason  for  what  must 
happen.  She  may  see  objects  side  by  side;  but  she 
cannot  see  a  reason  why  they  must  ever  be  side  by  side. 
She  finds  certain  events  to  occur  in  succession ;  but  the 
succession  supplies,  in  its  occurrence,  no  reason  for  its 
recurrence.  She  contemplates  external  objects  ;  but  she 
cannot  detect  any  internal  bond,  which  indissolubly 
connects  the  future  with  the  past,  the  possible  with  the 
real.  To  learn  a  proposition  by  experience,  and  to  see  it 
to  be  necessarily  true,  are  two  altogether  different  pro- 
cesses of  thought. 

2.  But  it  may  be  said,  that  we  do  learn  by  means  of 
observation  and  experience  many  universal  truths; 
indeed,  all  the  general  truths  of  which  science  consists. 
Is  not  the  doctrine  of  universal  gravitation  learnt  by 
experience  ?  Are  not  the  laws  of  motion,  the  properties 
of  light,  the  general  principles  of  chemistry  so  learnt? 
How,  with  these  examples  before  us,  can  we  say  that 
experience  teaches  no  universal  truths  ? 

To  this  we  reply,  that  these  truths  can  only  be 
known  to  be  general,  not  universal,  if  they  depend  upon 
experience  alone.  Experience  cannot  bestow  that  uni- 
versality which  she  herself  cannot  have,  and  that  necessity 
of  which  she  has  no  comprehension.  If  these  doctrines 
are  universally  true,  this  universality  flows  from  the  ideas 
which  we  apply  to  our  experience,  and  which  are,  as  we 
have  seen,  the  real  sources  of  necessary  truth.  How  far 
these  ideas  can  communicate  their  universality  and 
necessity  to  the  results  of  experience,  it  will  hereafter  be 
our  business  to  consider.  It  will  then  appear,  that  when 
the  mind  collects  from  observation  truths  of  a  wide  and 
comprehensive  kind,  which  approach  to  the  simplicity 
and  universality  of  the  truths  of  pure  science  ;  she  gives 


OF   IDEAS   IN   GENERAL. 

them  this  character  by  throwing  upon  them  the  light  of 
her  own  Fundamental  Ideas. 

But  the  truths  which  we  discover  by  observation  of 
the  external  world,  even  when  most  strikingly  simple 
and  universal,  are  not  necessary  truths.     Is  the  doctrine 
of  universal  gravitation  necessarily  true  ?     It  was  doubted 
by  Clairaut  (so  far  as  it  refers  to  the  moon),  when  the  pro- 
gression of  the  apogee  in  fact  appeared  to  be  twice  as 
great  as  the  theory  admitted.     It  has  been  doubted,  even 
more  recently,  with  respect  to  the  planets,  their  mutual 
perturbations  appearing  to  indicate  a  deviation  from  the 
law.     It  is  doubted  still,  by  some  persons,  with  respect 
to  the  double  stars.     But  suppose  all  these  doubts  to  be 
banished,  and  the  law  to  be  universal ;    is  it  then  proved 
to  be  necessary  ?     Manifestly  not :  the  very  existence  of 
these  doubts  proves  that  it  is  not  so.    For  the  doubts  were 
dissipated  by  reference  to  observation  and  calculation, 
not  by  reasoning  on  the  nature  of  the  law.     Clairaut's 
difficulty  was  removed  by  a  more  exact  calculation  of 
the  effect  of  the  sun's  force  on  the  motion  of  the  apogee. 
The  suggestion   of  Bessel,   that   the  intensity    of  gra- 
vitation  might   be   different  for   different  planets,    was 
found  to   be   unnecessary,   when   Professor   Airy    gave 
a  more  accurate  determination  of  the  mass  of  Jupiter. 
And  the  question  whether  the  extension  of  the  law  of 
the  inverse  square  to  the  double  stars  be  true,  (one  of 
the  most  remarkable  questions  now  before  the  scientific 
world,)   must    be    answered,    not    by   any  speculations 
concerning  what  the  laws  of  attraction  must  necessarily 
be,  but  by  carefully  determining  the  laws  of  the  motion 
of  these  curious   objects,  by  means  of  the  observations 
such  as  those  which  Sir  John  Herschel  has  collected  for 
that  purpose,  by  his  unexampled  survey  of  both  hemi- 
spheres of  the  sky.     And  since  the  extent  of  this  truth  is 


OF   EXPERIENCE.  63 

thus  to  be  determined  by  reference  to  observed  facts,  it 
is  clear  that  no  mere  accumulation  of  them  can  make  its 
universality  certain,  or  its  necessity  apparent. 

Thus  no  knowledge  of  the  necessity  of  any  truths 
can  result  from  the  observation  of  what  really  happens. 
This  being  clearly  understood,  we  are  led  to  an  import- 
ant inquiry. 

The  characters  of  universality  and  necessity  in  the 
truths  which  form  part  of  our  knowledge,  can  never 
be  derived  from  the  experience  by  which  so  large  a 
part  of  our  knowledge  is  obtained.  But  since,  as  we 
have  seen,  we  really  do  possess  a  large  body  of  truths 
which  are  necessary,  and  because  necessary,  therefore 
universal,  the  question  still  recurs,  from  what  source 
these  characters  of  universality  and  necessity  are 
derived. 

The  answer  to  this  question  we  will  attempt  to  give 
in  the  next  chapter. 


CHAPTER  XI. 
OF  THE  GROUNDS  OF  NECESSARY  TRUTHS. 

1.  To  the  question  just  stated,  I  reply,  that  the  necessity 
and  universality  of  the  truths  which  form  a  part  of  our 
knowledge,  are  derived  from  the  Fundamental  Ideas  which 
those  truths  involve.  These  ideas  entirely  shape  and  cir- 
cumscribe our  knowledge ;  they  regulate  the  active  opera- 
tions of  our  minds,  without  which  our  passive  sensations 
do  not  become  knowledge.  They  govern  these  operations, 
according  to  rules  which  are  not  only  fixed  and  perma- 
nent, but  which  may  be  expressed  in  plain  and  definite 
terms;  and  these  rules,  when  thus  expressed,  may  be  made 
the  basis  of  demonstrations  by  which  the  necessary  rela- 
tions imparted  to  our  knowledge  by  our  ideas  may  be 


64  OF   IDEAS   IN   GENERAL. 

traced  to  their  consequences  in  the  most  remote  ramifi- 
cations of  scientific  truth. 

These  enunciations  of  the  necessary  and  evident  con- 
ditions imposed  upon  our  knowledge  by  the  fundamental 
ideas  which  it  involves,  are  termed  Axioms.  Thus  the 
Axioms  of  Geometry  express  the  necessary  conditions 
which  result  from  the  idea  of  space;  the  Axioms  of 
Mechanics  express  the  necessary  conditions  which  flow 
from  the  ideas  of  force  and  motion ;  and  so  on. 

2.  It  will  be  the  office  of  several  of  the  succeeding 
Books  of  this  work  to  establish  and  illustrate  in  detail  what 
I  have  thus  stated  in  general  terms :  I  shall  there  pass  in 
review  many  of  the  most  important  fundamental  ideas 
on  which  the  existing  body  of  our  science  depends ;  and 
I  shall  endeavour  to  show,  for  each  such  idea  in  succes- 
sion, that  knowledge  involves  an  active  as  well  as  a  passive 
element;  that  it  is  not  possible  without  an  act  of  the 
mind,  regulated  by  certain  laws.     I  shall  further  attempt 
to  enumerate  some  of  the  principal  fundamental  relations 
which  each  idea  thus  introduces  into  our  thoughts,  and 
to  express  them  by  means  of  definitions  and  axioms,  and 
other  suitable  forms. 

I  will  only  add  a  remark  or  two  to  illustrate  further 
this  view  of  the  ideal  grounds  of  our  knowledge. 

3.  To  persons  familiar  with  any  of  the  demonstrative 
sciences,  it  will  be  apparent  that  if  we  state  all  the  Defini- 
tions and  Axioms  which  are  employed  in  the  demon- 
strations,   we    state    the   whole    basis    on   which   those 
reasonings  rest.     For  the  whole  process  of  demonstrative 
or  deductive  reasoning  in  any  science,  (as  in  geometry,  for 
instance,)  consists  entirely  in  combining  some  of  these 
first  principles  so  as  to  obtain  the  simplest  propositions  of 
the  science ;  then  combining  these  so  as  to  obtain  other 
propositions  of  greater  complexity;  and  so  on,  till  we 
advance  to  the  most  recondite  demonstrable  truths ;  these 


GROUNDS   OF    NECESSARY   TRUTHS.  65 

last,  however  intricate  and  unexpected,  still  involving  no 
principles  except  the  original  definitions  and  axioms. 
Thus,  by  combining  the  definition  of  a  triangle,  and  of 
equal  lines  and  equal  angles,  namely,  that  they  are  such 
as  when  applied  to  each  other,  coincide,  with  the  axiom 
respecting  straight  lines  (that  two  such  lines  cannot 
inclose  a  space,)  we  demonstrate  the  equality  of  triangles, 
under  certain  assumed  conditions.  Again,  by  combining 
this  result  with  the  definition  of  parallelograms,  and  with 
the  axiom  that  if  equals  be  taken  from  equals  the  wholes 
are  equal,  we  prove  the  equality  of  parallelograms  between 
the  same  parallels  and  upon  the  same  base.  From  this 
proposition,  again,  we  prove  the  equality  of  the  square  on 
the  hypotenuse  of  a  triangle  to  the  squares  on  the  two 
sides  containing  the  right  angle.  But  in  all  this  there  is 
nothing  contained  which  is  not  rigorously  the  result  of 
our  geometrical  definitions  and  axioms.  All  the  rest  of 
our  treatises  of  geometry  consists  only  of  terms  and 
phrases  of  reasoning,  the  object  of  which  is  to  connect 
those  first  principles,  and  to  exhibit  the  effects  of  their 
combination  in  the  shape  of  demonstration. 

4.  This  combination  of  first  principles  takes  place 
according  to  the  forms  and  rules  of  Logic.  All  the  steps 
of  the  demonstration  may  be  stated  in  the  shape  in  which 
logicians  are  accustomed  to  exhibit  processes  of  reasoning 
in  order  to  show  their  conclusiveness,  that  is,  in  Syllo- 
gisms. Thus  our  geometrical  reasonings  might  be  resolved 
into  such  steps  as  the  following : — 

All  straight  lines  drawn  from  the  centre  of  a  circle  to 
its  circumference  are  equal : 

But  the  straight  lines  AB,  AC,  are  drawn  from  the 
centre  of  a  circle  to  its  circumference : 

Therefore  the  straight  lines  A B,  AC,  are  equal. 

Each  step  of  geometrical,  and  all  other  demonstrative 
reasoning,  may  be  resolved  into  three  such  clauses  as 
VOL.  i.  F 


66  OF   IDEAS   IN    GENERAL. 

these ;  and  these  three  clauses  are  termed  respectively, 
the  major  premiss,  the  minor  premiss,  and  the  conclusion ; 
or,  more  briefly,  the  major,  the  minor,  and  the*  con- 
clusion. 

The  principle  which  justifies  the  reasoning  when  exhi- 
bited in  this  syllogistic  form,  is  this : — that  a  truth  which 
can  be  asserted  as  generally,  or  rather  as  universally  true, 
can  be  asserted  as  true  also  in  each  particular  case.  The 
minor  only  asserts  a  certain  particular  case  to  be  an 
example  of  such  conditions  as  are  spoken  of  in  the  major; 
and  hence  the  conclusion,  which  is  true  of  the  major  by 
supposition,  is  true  of  the  minor  by  consequence ;  and 
thus  we  proceed  from  syllogism  to  syllogism,  in  each  one 
employing  some  general  truth  in  some  particular  instance. 
Any  proof  which  occurs  in  geometry,  or  any  other 
science  of  demonstration,  may  thus  be  reduced  to  a  series 
of  processes,  in  each  of  which  we  pass  from  some  gene- 
ral proposition  to  the  narrower  and  more  special  propo- 
sitions which  it  includes.  And  this  process  of  deriving 
truths  by  the  mere  combination  of  general  principles, 
applied  in  particular  hypothetical  cases,  is  called  deduc- 
tion ;  being  opposed  to  induction,  in  which,  as  we  have 
seen,  a  new  general  principle  is  introduced  at  every  step. 

5.  Now  we  have  to  remark  that,  this  being  so,  however 
far  we  follow  such  deductive  reasoning,  we  can  never  have 
in  our  conclusion  any  truth  which  is  not  virtually  included 
in  the  original  principles  from  which  the  reasoning  started. 
For  since  at  any  step  we  merely  take  out  of  a  general 
proposition  something  included  in  it,  while  at  the  pre- 
ceding step  we  have  taken  this  general  proposition  out  of 
one  more  general,  and  so  on  perpetually,  it  is  manifest 
that  our  last  result  was  really  included  in  the  principle 
or  principles  with  which  we  began.  I  say  principles, 
because,  although  our  logical  conclusion  can  only  exhibit 
the  legitimate  issue  of  our  first  principles,  it  may,  never- 


GROUNDS   OF   NECESSARY   TRUTHS.  67 

theless,  contain  the  result  of  the  combination  of  several 
such  principles,  and  may  thus  assume  a  great  degree  of 
complexity,  and  may  appear  so  far  removed  from  the 
parent  truths,  as  to  betray  at  first  sight  hardly  any  rela- 
tionship with  them.  Thus  the  proposition  which  has 
already  been  quoted  respecting  the  squares  on  the  sides 
of  a  right-angled  triangle,  contains  the  results  of  many 
elementary  principles ;  as  the  definitions  of  parallels,  tri- 
angle, and  square ;  the  axioms  respecting  straight  lines, 
and  respecting  parallels ;  and,  perhaps,  others.  The  con- 
clusion is  complicated  by  containing  the  effects  of  the 
combination  of  all  these  elements;  but  it  contains  no- 
thing, and  can  contain  nothing,  but  such  elements  and 
their  combinations. 

This  doctrine,  that  logical  reasoning  produces  no  new 
truths,  but  only  unfolds  and  brings  into  view  those  truths 
which  were,  in  effect,  contained  in  the  first  principles  of 
the  reasoning,  is  assented  to  by  almost  all  who,  in  modern 
times,  have  attended  to  the  science  of  logic.  Such  a  view 
is  admitted  both  by  those  who  defend,  and  by  those  who 
depreciate  the  value  of  logic.  "  Whatever  is  established 
by  reasoning,  must  have  been  contained  and  virtually 
asserted  in  the  premises*,"  "  The  only  truth  which  such 
propositions  can  possess  consists  in  conformity  to  the 
original  principles." 

In  this  manner  the  whole  substance  of  our  geo- 
metry is  reduced  to  the  definitions  and  axioms  which  we 
employ  in  our  elementary  reasonings ;  and  in  like  manner 
we  reduce  the  demonstrative  truths  of  any  other  science 
to  the  definitions  and  axioms  which  we  there  employ. 

6.  But  in  reference  to  this  subject,  it  has  sometimes 
been  said  that  demonstrative  sciences  do  in  reality  depend 
upon  Definitions  only;  and  that  110  additional  kind  of 

*  WHATELEY'S  Logic,  pp.  237,  238. 

F  2 


68  OF   IDEAS    IN    GENERAL. 

principle,  such  as  we  have  supposed  Axioms  to  be,  is 
absolutely  required.  It  has  been  asserted  that  in  geo- 
metry, for  example,  the  source  of  the  necessary  truth  of 
our  propositions  is  this,  that  they  depend  upon  definitions 
alone,  and  consequently  merely  state  the  identity  of  the 
same  thing  under  different  aspects. 

That  in  the  sciences  which  admit  of  demonstration,  as 
geometry,  mechanics,  and  the  like,  axioms  as  well  as  defi- 
nitions are  needed,  in  order  to  express  the  grounds  of 
our  necessary  convictions,  must  be  shown  hereafter  by  an 
examination  of  each  of  these  sciences  in  particular.  But 
that  the  propositions  of  these  sciences,  those  of  geometry 
for  example,  do  not  merely  assert  the  identity  of  the  same 
thing,  will,  I  think,  be  generally  allowed,  if  we  consider 
the  assertions  which  we  are  enabled  to  make.  When 
we  declare  that  "  a  straight  line  is  the  shortest  distance 
between  two  points,"  is  this  merely  an  identical  proposi- 
tion ?  the  definition  of  a  straight  line  in  another  form  ? 
Not  so :  the  definition  of  a  straight  line  involves  the 
notion  of  form  only,  and  does  not  contain  anything  about 
magnitude;  consequently,  it  cannot  contain  anything 
equivalent  to  "  shortest."  Thus  the  propositions  of  geo- 
metry are  not  merely  identical  propositions;  nor  have 
we  in  their  general  character  anything  to  countenance 
the  assertion,  that  they  are  the  results  of  definitions 
alone.  And  when  we  come  to  examine  this  and  other 
sciences  more  closely,  we  shall  find  that  axioms,  such  as 
are  usually  in  our  treatises  made  the  fundamental  prin- 
ciples of  our  demonstrations,  neither  have  ever  been,  nor 
can  be,  dispensed  with.  Axioms,  as  well  as  definitions, 
are  in  all  cases  requisite,  in  order  properly  to  exhibit  the 
grounds  of  necessary  truth. 

7.  Thus  the  real  logical  basis  of  every  body  of  demon- 
strated truths  are  the  Definitions  and  Axioms  which  are 
the  first  principles  of  the  reasonings.  But  when  we  are 


GROUNDS  OF  NECESSARY  TRUTHS.          69 

arrived  at  this  point,  the  question  further  occurs,  what  is 
the  ground  of  the  truth  of  these  Axioms  ?  It  is  not  the 
logical  but  the  philosophical,  not  the  formal  but  the  real 
foundation  of  necessary  truth,  which  we  are  seeking. 
Hence  this  inquiry,  What  is  the  ground  of  the  axioms  of 
geometry,  of  mechanics,  and  of  any  other  demonstrable 
science,  necessarily  comes  before  us. 

The  answer  which  we  are  led  to  give,  by  the  view 
which  we  have  taken  of  the  nature  of  knowledge,  has 
already  been  stated.  The  ground  of  the  axioms  belong- 
ing to  each  science  is  the  idea  which  the  axiom  involves. 
The  ground  of  the  axioms  of  geometry  is  the  idea  of 
space:  the  ground  of  the  axioms  of  mechanics  is  the 
idea  of  force,  of  action  and  reaction,  and  the  like.  And 
hence  these  ideas  are  Fundamental  Ideas;  and  since 
they  are  thus  the  foundations,  not  only  of  demonstration 
but  of  truth,  an  examination  into  their  real  import  and 
nature  is  of  the  greatest  consequence  to  our  purpose. 

8.  Not  only  the  Axioms,  but  the  Definitions  which 
form  the  basis  of  our  reasonings,  depend  upon  our  Funda- 
mental Ideas.  And  the  definitions  are  not  arbitrary  defi- 
nitions, but  are  determined  by  a  necessity  no  less  rigorous 
than  the  axioms  themselves.  We  could  not  think  of 
geometrical  truths  without  conceiving  a  circle;  and  we 
could  not  reason  concerning  such  truths  without  defining 
a  circle  in  some  mode  equivalent  to  that  which  is  com- 
monly adopted.  The  definitions  of  parallels,  of  right 
angles,  and  the  like,  are  quite  as  necessarily  prescribed 
by  the  nature  of  the  case,  as  the  axioms  which  these  defi- 
nitions bring  with  them.  Indeed  we  may  substitute  one 
of  these  kinds  of  principles  for  another.  We  cannot 
always  put  a  definition  in  the  place  of  an  axiom ;  but  we 
may  always  find  an  axiom  which  shall  take  the  place  of 
a  definition.  If  we  assume  a  proper  axiom  respecting 
straight  lines,  we  need  no  definition  of  a  straight  line. 


70  OF   IDEAS   IN   GENERAL. 

But  in  whatever  shape  the  principle  appear,  as  definition 
or  as  axiom,  it  has  about  it  nothing  casual  or  arbitrary, 
but  is  determined  to  be  what  it  is,  as  to  its  import,  by  the 
most  rigorous  necessity,  growing  out  of  the  Idea  of  Space. 

7.  These  principles, — definitions,  and  axioms, — thus 
exhibiting  the  primary  developements  of  a  fundamental 
idea,  do  in  fact  express  the  idea,  so  far  as  its  expression 
in  words  forms  part  of  our  science.  They  are  different 
views  of  the  same  body  of  truth ;  and  though  each  prin- 
ciple, by  itself,  exhibits  only  one  aspect  of  this  body, 
taken  together  they  convey  a  sufficient  conception  of  it 
for  our  purposes.  The  idea  itself  cannot  be  fixed  in 
words  ;  but  these  various  lines  of  truth  proceeding  from 
it,  suggest  sufficiently  to  a  fitly-prepared  mind,  the  place 
where  the  idea  resides,  its  nature,  and  its  efficacy. 

It  is  true  that  these  principles, — our  elementary  defi- 
nitions and  axioms, — even  taken  altogether,  express  the 
idea  incompletely.  Thus  the  definitions  and  axioms  of 
geometry,  as  they  are  stated  in  our  elementary  works,  do 
not  fully  express  the  idea  of  space  as  it  exists  in  our 
minds.  For,  in  addition  to  these,  other  axioms,  indepen- 
dent of  these,  and  no  less  evident,  can  be  stated ;  and  are 
in  fact  stated  when  we  come  to  the  higher  geometry. 
Such,  for  instance,  is  the  axiom  of  Archimedes — that  a 
curve  line  which  joins  two  points  is  less  than  a  broken 
line  which  joins  the  same  points  and  includes  the  curve. 
And  thus  the  idea  is  disclosed  but  not  fully  revealed, 
imparted  but  not  transfused,  by  the  use  we  make  of  it 
in  science.  When  we  have  taken  from  the  fountain  so 
much  as  serves  our  purpose,  there  still  remains  behind  a 
deep  well  of  truth,  which  we  have  not  exhausted,  and 
which  we  may  easily  believe  to  be  inexhaustible, 


71 


CHAPTER  XII. 

THE  FUNDAMENTAL  IDEAS  ARE  NOT  DERIVED 
FROM  EXPERIENCE. 

1.  BY  the  course  of  speculation  contained  in  the  last 
three  Chapters,  we  are  again  led  to  the  conclusion  which 
we  have  already  stated,  that  our  knowledge  contains  an 
ideal  element,  and  that  this  element  is  not  derived  from 
experience.     For  we  have  seen  that  there  are  proposi- 
tions which  are  known  to  be  necessarily  true ;  and  that 
such  knowledge  is  not,  and  cannot  be,  obtained  by  mere 
observation  of  actual  facts.    It  has  been  shown,  also,  that 
these  necessary  truths  are  the  results  of  certain  funda- 
mental ideas,  such  as  those  of  space,  number,  and  the 
like.     Hence  it  follows  inevitably  that  these  ideas  and 
others  of  the  same  kind  are  not  derived  from  experience. 
For  these  ideas  possess  a  power  of  infusing  into  their 
developements  that  very  necessity  which  experience  can 
in  no  way  bestow.     This  power  they  do  not  borrow  from 
the  external  world,  but  possess  by  their  own  nature.    Thus 
we  unfold  out  of  the  idea  of  space  the  propositions  of 
geometry,  which  are  plainly  truths  of  the  most  rigorous 
necessity  and  universality.     But  if  the  idea  of  space  were 
merely  collected  from  observation  of  the  external  world, 
it  could  never  enable  or  entitle  us  to  assert  such  proposi- 
tions :  it  could  never  authorize  us  to  say  that  not  merely 
some  lines,  but  all  lines,  not  only  have,  but  must  have, 
those  properties  which  geometry  teaches.     Geometry  in 
every  proposition  speaks  a  language   which  experience 
never  dares  to  utter;  and  indeed  of  which  she  but  half 
comprehends  the  meaning.     Experience  sees   that   the 
assertions  are  true,  but  she  sees  not  how  profound  and 
absolute  is   their  truth.     She  unhesitatingly  assents   to 
the  laws  which  geometry  delivers,  but  she  does  not  pre- 


72  OF    IDEAS   IN    GENERAL. 

tend  to  see  the  origin  of  their  obligation.  She  is  always 
ready  to  acknowledge  the  sway  of  pure  scientific  prin- 
ciples as  a  matter  of  fact,  but  she  does  not  dream  of  offer- 
ing her  opinion  on  their  authority  as  a  matter  of  right ; 
still  less  can  she  justly  claim  to  be  herself  the  source  of 
that  authority. 

David  Hume  asserted*,  that  we  are  incapable  of  seeing 
in  any  of  the  appearances  which  the  world  presents  any- 
thing of  necessary  connexion ;  and  hence  he  inferred  that 
our  knowledge  cannot  extend  to  any  such  connexion. 
It  will  be  seen  from  what  we  have  said  that  we  assent  to 
his  remark  as  to  the  fact,  but  we  differ  from  him  alto- 
gether in  the  consequence  to  be  drawn  from  it.  Our 
inference  from  Hume's  observation  is,  not  the  truth  of 
his  conclusion,  but  the  falsehood  of  his  premises ; — not 
that,  therefore,  we  can  know  nothing  of  natural  con- 
nexion, but  that,  therefore,  we  have  some  other  source  of 
knowledge  than  experience : — not  that  we  can  have  no 
idea  of  connexion  or  causation,  because,  in  his  language, 
it  cannot  be  the  copy  of  an  impression ;  but  that  since 
we  have  such  an  idea,  our  ideas  are  not  the  copies  of  our 
impressions. 

Since  it  thus  appears  that  our  fundamental  ideas  are 
not  acquired  from  the  external  world  by  our  senses,  but 
have  some  separate  and  independent  origin,  it  is  import- 
ant for  us  to  examine  their  nature  and  properties,  as  they 
exist  in  themselves,  and  this  it  will  be  our  business  to  do 
through  a  portion  of  the  following  pages.  But  it  may  be 
proper  first  to  notice  one  or  two  objections  w7hich  may 
possibly  occur. 

3.  It  may  be  said  that  without  the  use  of  our  senses, 
of  sight  and  touch,  for  instance,  we  should  never  have  any 
idea  of  space ;  that  this  idea,  therefore,  may  properly  be 
said  to  be  derived  from  those  senses.  And  to  this  I  reply 

*  Essay S)  vol.  ii.  p.  70. 


FUNDAMENTAL   IDEAS   NOT   DERIVATIVE.  73 

by  referring  to  a  parallel  instance.     Without  light  we 
should    have   no   perception   of  visible   figure;  yet   the 
power  of  perceiving  visible  figure  cannot  be   said  to  be 
derived  from  the  light,  but  resides  in  the  structure  of  the 
eye.     If  we  had  never  seen  objects  in  the  light,  we  should 
be  quite  unaware  that  we  possessed  a  power  of  vision ;  yet 
we  should  not  possess  it  the  less  on  that  account.     If  we 
had  never  exercised  the  senses  of  sight  and  touch  (if  we 
can  conceive  such  a  state  of  human  existence)  we  know 
not  that  we  should  be  conscious  of  an  idea   of  space. 
But  the  light  reveals  to  us  at  the  same  time  the  existence 
of  external  objects  and  our  own  power  of  seeing.      And 
in  a  very  similar  manner,  the  exercise  of  our  senses  dis- 
closes to  us,  at  the  same  time,  the  external  world,  and 
our  own  ideas  of  space,  time,  and  other  conditions,  with- 
out which  the  external  world  can  neither  be  observed  nor 
conceived.     That  light  is  necessary  to  vision,  does  not,  in 
any  degree,  supersede  the  importance  of  a  separate  exa- 
mination of  the  laws  of  our  visual  powers,  if  we  would 
understand  the  nature  of  our  own   bodily  faculties   and 
the  extent  of  the  information  they  can  give  us.     In  like 
manner,  the  fact  that  intercourse  with  the  external  world 
is  necessary  for  the  conscious   employment  of  our  ideas^ 
does  not  make  it  the  less  essential  for  us  to  examine  those 
ideas  in  their  most  intimate  structure,  in   order  that  we 
may  understand  the  grounds  and  limits   of  our  know- 
ledge.    Even  before  we  see  a  single  object,  we  have  a 
faculty  of  vision ;  and  in  like  manner,  if  we  can  suppose 
a  man  who  has  never  contemplated  an  object  in  space  or 
time,  we  must  still  assume  him  to  have  the  faculties  of 
entertaining  the  ideas  of  space  and  time,  which  faculties 
are  called  into  play  on  the  very  first  occasion  of  the  use 
of  the  senses. 

4.  In  answer  to   such  remarks  as  the  above,  it  has 
sometimes  been  said  that  to  assume  separate  faculties  in 


74  OF   IDEAS   IN   GENERAL. 

the  mind  for  so  many  different  processes  of  thought,  is  to 
give  a  mere  verbal  explanation,  since  we  learn  nothing 
concerning  our  idea  of  space  by  being  told  that  we  have 
a  faculty  of  forming  such  an  idea.  It  has  been  said  that 
this  course  of  explanation  leads  to  an  endless  multipli- 
cation of  elements  in  man's  nature,  without  any  advan- 
tage to  our  knowledge  of  his  true  constitution.  We 
may,  it  is  said,  assert  man  to  have  a  faculty  of  walking, 
of  standing,  of  breathing,  of  speaking ;  but  what,  it  is 
asked,  is  gained  by  such  assertions  ?  To  this  I  reply,  that 
we  undoubtedly  have  such  faculties  as  those  just  named ; 
that  it  is  by  no  means  unimportant  to  consider  them ;  and 
that  the  main  question  in  such  cases  is,  whether  they  are 
separate  and  independent  faculties,  or  complex  and  deri- 
vative ones ;  and,  if  the  latter  be  the  case,  what  are  the 
simple  and  original  faculties  by  the  combination  of  which 
the  others  are  produced.  In  walking,  standing,  breath- 
ing, for  instance,  a  great  part  of  the  operation  can  be  re- 
duced to  one  single  faculty ;  the  voluntary  exercise  of  our 
muscles.  But  in  breathing  this  does  not  appear  to  be 
the  whole  of  the  process.  The  operation  is,  in  part  at 
least,  involuntary ;  and  it  has  been  held  that  there  is  a 
certain  sympathetic  action  of  the  nerves,  in  addition  to 
the  voluntary  agency  which  they  transmit,  which  is  essen- 
tial to  the  function.  To  determine  whether  or  no  this 
sympathetic  faculty  is  real  and  distinct,  and  if  so,  what 
are  its  laws  and  limits,  is  certainly  a  highly  philosophical 
inquiry,  and  well  deserving  the  attention  which  has  been 
bestowed  upon  it  by  eminent  physiologists.  And  just  of 
the  same  nature  are  the  inquiries  with  respect  to  man's 
intellectual  constitution,  on  which  we  propose  to  enter. 
For  instance,  man  has  a  faculty  of  apprehending  time,  and 
a  faculty  of  reckoning  numbers ;  are  these  distinct,  or  is 
one  faculty  derived  from  the  other?  To  analyse  the  vari- 
ous combinations  of  our  ideas  and  observations  into  the 


FUNDAMENTAL   IDEAS   NOT   DERIVATIVE.  75 

original  faculties  which  they  involve ;  to  show  that  these 
faculties  are  original,  and  not  capable  of  further  analysis ; 
to  point  out  the  characters  which  mark  these  faculties 
and  lead  to  the  most  important  features  of  our  know- 
ledge ; — these  are  the  kind  of  researches  on  which  we 
have  now  to  enter,  and  these,  we  trust,  will  be  found 
to  be  far  from  idle  or  useless  parts  of  our  plan.  If  we 
succeed  in  such  attempts,  it  will  appear  that  it  is  by 
no  means  a  frivolous  or  superfluous  step  to  distinguish 
separate  faculties  in  the  mind.  If  we  do  not  learn  much 
by  being  told  that  we  have  a  faculty  of  forming  the  idea 
of  space,  we  at  least,  by  such  a  commencement,  circum- 
scribe a  certain  portion  of  the  field  of  our  investigations, 
which,  we  shall  afterwards  endeavour  to  show,  requires 
and  rewards  a  special  examination.  And  though  we  shall 
thus  have  to  separate  the  domain  of  our  philosophy  into 
many  provinces,  these  are,  as  we  trust  it  will  appear, 
neither  arbitrarily  assigned,  nor  vague  in  their  limits,  nor 
infinite  in  number. 


CHAPTER  XIII. 
OF  THE  PHILOSOPHY  OF  THE  SCIENCES. 

s 

WE  proceed,  in  the  ensuing  Books,  to  the  closer 
examination  of  a  considerable  number  of  those  Funda- 
mental Ideas  on  which  the  sciences,  hitherto  most  suc- 
cessfully cultivated,  are  founded.  In  this  task,  our 
objects  will  be  to  explain  and  analyse  such  Ideas  so  as 
to  bring  into  view  the  Definitions  and  Axioms,  or  other 
forms,  in  which  we  may  clothe  the  conditions  to  which 
our  speculative  knowledge  is  subjected.  I  shall  also 
try  to  prove,  for  some  of  these  Ideas  in  particular,  what 
has  been  already  urged  respecting  them  in  general,  that 


76  OF   IDEAS   IN   GENERAL. 

they  are  not  derived  from  observation,  but  necessarily 
impose  their  conditions  upon  that  knowledge  of  which 
observation  supplies  the  materials.  I  shall  further,  in 
some  cases,  endeavour  to  trace  the  history  of  these  Ideas 
as  they  have  successively  come  into  notice  in  the  progress 
of  science ;  the  gradual  developement  by  which  they  have 
arrived  at  their  due  purity  and  clearness ;  and,  as  a  neces- 
sary part  of  such  a  history,  I  shall  give  a  view  of  some  of 
the  principal  controversies  which  have  taken  place  with 
regard  to  each  portion  of  knowledge. 

An  exposition  and  discussion  of  the  Fundamental 
Ideas  of  each  Science  may,  with  great  propriety,  be 
termed  the  PHILOSOPHY  of  such  science.  These  ideas 
contain  in  themselves  the  elements  of  those  truths 
which  the  science  discovers  and  enunciates ;  and  in  the 
progress  of  the  sciences,  both  in  the  world  at  large  and  in 
the  mind  of  each  individual  student,  the  most  important 
steps  consist  in  apprehending  these  ideas  clearly,  and  in 
bringing  them  into  accordance  with  the  observed  facts. 
I  shall,  therefore,  in  a  series  of  Books,  treat  of  the  Philo- 
sophy of  the  Pure  Sciences,  the  Philosophy  of  the  Mecha- 
nical Sciences,  the  Philosophy  of  Chemistry,  and  the  like, 
and  shall  analyse  and  examine  the  ideas  which  these 
sciences  respectively  involve. 

In  this  undertaking,  inevitably  somewhat  long,  and 
involving  many  deep  and  subtle  discussions,  I  shall  take, 
as  a  chart  of  the  country  before  me,  by  which  my  course 
is  to  be  guided,  the  scheme  of  the  sciences  which  I  was 
led  to  form  by  travelling  over  the  history  of  each  in 
order*.  Each  of  the  sciences  of  which  I  then  narrated 
the  progress,  depends  upon  several  of  the  Fundamental 
Ideas  of  which  I  have  to  speak :  some  of  these  Ideas  are 
peculiar  to  one  field  of  speculation,  others  are  common  to 
more.  A  previous  enumeration  of  Ideas  thus  collected 
*  History  of  the  Inductive  Sciences. 


PHILOSOPHY    OF    SCIENCES.  77 

may  serve  both  to  show  the  course  and  limits  of  this  part 
of  our  plan,  and  the  variety  of  interest  which  it  offers. 

I  shall,  then,  successively,  have  to  speak  of  the  ideas 
which  are  the  foundation  of  geometry  and  arithmetic, 
(and  which  also  regulate  all  sciences  depending  upon 
these,  as  astronomy  and  mechanics;)  namely,  the  ideas 
of  space,  time,  and  number : 

Of  the  ideas  on  which  the  mechanical  sciences  (as 
mechanics,  hydrostatics,  physical  astronomy)  more  pecu- 
liarly rest ;  the  ideas  of  force  and  matter,  or  rather  the 
idea  of  cause,  which  is  the  basis  of  these : 

Of  the  ideas  which  the  secondary  mechanical  sciences 
(acoustics,  optics,  and  thermotics)  involve;  namely,  the 
ideas  of  the  externality  of  objects,  and  of  the  media  by 
which  we  perceive  their  qualities  : 

Of  the  ideas  which  are  the  basis  of  mechanico-chemi- 
cal  and  chemical  science,  polarity,  chemical  affinity,  and 
substance;  and  the  idea  of  symmetry,  a  necessary  part  of 
the  philosophy  of  crystallography : 

Of  the  ideas  on  which  the  classificatory  sciences  pro- 
ceed (mineralogy,  botany,  and  zoology) ;  namely,  the  ideas 
of  resemblance,  arid  of  its  gradations,  and  of  natural 
affinity: 

Finally,  of  those  ideas  on  which  the  physiological 
sciences  are  founded ;  the  ideas  of  separate  vital  powers, 
such  as  assimilation  and  irritability ;  and  the  idea  of  final 
cause. 

We  have,  besides  these,  the  Palsetiological  sciences, 
which  proceed  mainly  on  the  conception  of  historical 
causation. 

It  is  plain  that  when  we  have  proceeded  so  far  as 
this,  we  have  advanced  to  the  verge  of  those  speculations 
which  have  to  do  with  mind  as  well  as  body.  The 
extension  of  our  philosophy  to  such  a  field,  if  it  can  be 
justly  so  extended,  will  be  one  of  the  most  important 


78  OF   IDEAS    IN   GENERAL. 

results  of  our  researches ;  but  on  that  very  account  we 
must  fully  study  the  lessons  which  we  learn  in  those 
fields  of  speculation  where  our  doctrines  are  most  secure, 
before  we  venture  into  a  region  where  our  principles  will 
appear  to  be  more  precarious,  and  where  they  are  inevi- 
tably less  precise. 

We  now  proceed  to  the  examination  of  the  above 
ideas,  and  to  such  essays  towards  the  philosophy  of  each 
science  as  this  course  of  investigation  may  suggest. 


79 


BOOK  II. 


THE   PHILOSOPHY    OF    THE   PURE 
SCIENCES. 


CHAPTER  I. 
OF    THE    PURE    SCIENCES. 

1.  ALL  external  objects  and  events  which  we  can 
contemplate  are  viewed  as  having  relations  of  Space, 
Time,  and  Number;  and  are  subject  to  the  general 
conditions  which  these  Ideas  impose,  as  well  as  to  the 
particular  laws  which  belong  to  each  class  of  objects  and 
occurrences.  The  special  laws  of  nature,  considered  under 
the  various  aspects  which  constitute  the  different  sciences, 
are  obtained  by  a  mixed  reference  to  experience  and  to 
the  fundamental  ideas  of  each  science.  But  besides  the 
sciences  thus  formed  by  the  aid  of  special  experience,  the 
conditions  which  flow  from  those  more  comprehensive 
ideas  first  mentioned,  space,  time,  and  number,  constitute 
a  body  of  science,  applicable  to  objects  and  changes  of 
all  kinds,  and  deduced  without  recurrence  being  had  to 
any  observation  in  particular.  These  sciences,  thus 
unfolded  out  of  ideas  alone,  unmixed  with  any  reference 
to  the  phenomena  of  matter,  are  hence  termed  pure 
sciences.  The  principal  sciences  of  this  class  are  geome- 
try, theoretical  arithmetic,  and  algebra  considered  in  its 
most  general  sense,  as  the  investigation  of  the  relations 
of  space  and  number  by  means  of  general  symbols. 


80  PHILOSOPHY   OF   THE   PURE    SCIENCES. 

2.  These  pure  sciences  were  not    included  in  our 
survey  of  the  history  of  the  sciences,  because  they  are 
not  inductive  sciences.     Their  progress  has  not  consisted 
in  collecting*  laws  from  phenomena,  true  theories  from 
observed  facts,  and  more  general  from  more  limited  laws ; 
but  in  tracing  the  consequences  of  the  ideas  themselves, 
and  in  detecting  the  most  general  and  intimate  analogies 
and  connexions  which  prevail  among  such  conceptions  as 
are  derivable  from  the  ideas.     These  sciences  have  no 
principles  besides  definitions  and  axioms,  and  no  process 
of  proof  but  deduction ;  this  process,  however,  assuming 
here  a  most  remarkable  character ;  and  exhibiting  a  com- 
bination   of  simplicity  and   complexity,    of  rigour   and 
generality,  quite  unparalleled  in  other  subjects. 

3.  The  universality  of  the  truths,  and  the  rigour  of 
the   demonstrations   of    these   pure    sciences,   attracted 
attention  in  the  earliest  times ;  and  it  was  perceived  that 
they  offered  an  exercise  and  a  discipline  of  the  intellec- 
tual faculties,  in  a  form  peculiarly  free  from  admixture 
of  extraneous  elements.     They  were  strenuously  culti- 
vated by  the  Greeks,  both  with  a  view  to  such  a  disci- 
pline, and  from  the  love  of  speculative  truth  which  pre- 
vailed among  that  people:  and  the  name  mafliematics,  by 
which  they  are  designated,  indicates  this  their  character 
of  disciplined  studies. 

4.  As  has  already  been  said,  the  ideas  which  these 
sciences  involve  extend  to  all  the  objects  and  changes 
which  we  observe  in  the  external  world ;  and  hence  the 
consideration   of  mathematical   relations  forms  a  large 
portion  of  many  of  the  sciences  which  treat  of  the  phe- 
nomena  and   laws   of    external    nature,    as   astronomy, 
optics,  and  mechanics.     Such  sciences  are  hence  often 
termed  mixed  mathematics,  the   relations  of  space  and 
number  being,  in  these  branches  of  knowledge,  combined 
with    principles    collected    from     special    observation; 


OF   THE    IDEA    OF    SPACE.  81 

while  geometry,  algebra,  and  the  like  subjects,  which 
involve  no  result  of  experience,  are  called  pure  mathe- 
matics. 

5.  Space,  time,  and  number,  may  be  conceived  as 
forms  by  which  the  knowledge  derived  from  our  sensa- 
tions is  moulded,  and  which  are  independent  of  the  dif- 
ferences in  the  matter  of  our  knowledge,  arising  from  the 
sensations  themselves.  Hence  the  sciences  which  have 
these  ideas  for  their  subject  may  be  termed  formal 
sciences.  In  this  point  of  view,  they  are  distinguished 
from  sciences  in  which,  besides  these  mere  formal  laws 
by  which  appearances  are  corrected,  we  endeavour  to 
apply  to  the  phenomena  the  idea  of  cause,  or  some  of  the 
other  ideas  which  penetrate  further  into  the  principles 
of  nature.  We  have  thus,  in  the  History,  distinguished 
Formal  Astronomy  and  Formal  Optics  from  Physical 
Astronomy  and  Physical  Optics. 

We  now  proceed  to  our  examination  of  the  ideas 
which  constitute  the  foundation  of  these  formal  or  pure 
mathematical  sciences,  beginning  with  the  idea  of  space. 


CHAPTER  II. 
OF    THE    IDEA    OF    SPACE. 

1 .  BY  speaking  of  space  as  an  Idea,  I  intend  to  imply, 
as  has  already  been  stated,  that  the  apprehension  of 
objects  as  existing  in  space,  and  of  the  relations  of  posi- 
tion, &c.,  which  thus  prevail  among  them,  is  not  a  conse- 
quence of  experience,  but  a  result  of  a  peculiar  constitu- 
tion and  activity  of  the  mind,  which  is  independent  of  all 
experience  in  its  origin,  though  constantly  combined  with 
experience  in  its  exercise. 

That  the  idea  of  space  is  thus  independent  of  experi- 
ence, has  already  been  pointed  out  in  speaking  of  ideas 

VOL.    I.  G 


82  PHILOSOPHY    OF   THE   PURE   SCIENCES. 

in  general :  but  it  may  be  useful  to  illustrate  the  doctrine 
further  in  this  particular  case. 

I  assert,  then,  that  space  is  not  a  notion  obtained 
by  experience.  Experience  gives  us  information  con- 
cerning things  without  us:  but  our  apprehending  them 
as  without  us,  takes  for  granted  their  existence  in  space. 
Experience  acquaints  us  what  are  the  form,  position, 
magnitude  of  particular  objects :  but  that  they  have  form, 
position,  magnitude,  presupposes  that  they  are  in  space. 
We  cannot  derive  from  appearances,  by  the  way  of 
observation,  the  habit  of  representing  things  to  ourselves 
as  in  space ;  for  no  single  act  of  observation  is  possible 
any  otherwise  than  by  beginning  with  such  a  representa- 
tion, and  conceiving  objects  as  already  existing  in  space. 

2.  That  our  mode  of  representing  space  to  ourselves 
is  not  derived  from  experience,  is  clear  also  from  this : — 
that  through  this  mode  of  representation  we  arrive  at 
propositions  which  are  rigorously  universal  and  neces- 
sary. Propositions  of  such  a  kind  could  not  possibly  be 
obtained  from  experience ;  for  experience  can  only  teach 
us  by  a  limited  number  of  examples,  and  therefore  can 
never  securely  establish  a  universal  proposition :  and 
again,  experience  can  only  inform  us  that  anything  is  so, 
and  can  never  prove  that  it  must  be  so.  That  two  sides 
of  a  triangle  are  greater  than  the  third  is  a  universal  and 
necessary  geometrical  truth :  it  is  true  of  all  triangles ; 
it  is  true  in  such  a  way  that  the  contrary  cannot  be  con- 
ceived. Experience  could  not  prove  such  a  proposition. 
And  experience  has  not  proved  it ;  for  perhaps  no  man 
ever  made  the  trial  as  a  means  of  removing  doubts :  and 
no  trial  could,  in  fact,  add  in  the  smallest  degree  to  the 
certainty  of  this  truth.  To  seek  for  proof  of  geometrical 
propositions  by  an  appeal  to  observation  proves  nothing 
in  reality,  except  that  the  person  who  has  recourse  to  such 
grounds  has  no  due  apprehension  of  the  nature  of  geo- 


OF    THE    IDEA    OF    SPACE.  83 

metrical  demonstration.  We  have  heard  of  persons  who 
convinced  themselves  by  measurement  that  the  geome- 
trical rule  respecting  the  squares  on  the  sides  of  a  right- 
angled  triangle  was  true :  but  these  were  persons  whose 
minds  had  been  engrossed  by  practical  habits,  and  in 
whom  the  speculative  developement  of  the  idea  of  space 
had  been  stifled  by  other  employments.  The  practical 
trial  of  the  rule  may  illustrate,  but  cannot  prove  it. 
The  rule  will  of  course  be  confirmed  by  such  trial,  because 
what  is  true  in  general  is  true  in  particular :  but  it  cannot 
be  proved  from  any  number  of  trials,  for  no  accumulation 
of  particular  cases  makes  up  a  universal  case.  To  all 
persons  who  can  see  the  force  of  any  proof,  the  geome- 
trical rule  above  referred  to  is  as  evident,  and  its  evidence 
as  independent  of  experience,  as  the  assertion  that  sixteen 
and  nine  make  twenty-five.  At  the  same  time  the  truth 
of  the  geometrical  rule  is  quite  independent  of  numerical 
truths,  and  results  from  the  relations  of  space  alone. 
This  could  not  be  if  our  apprehension  of  the  relations  of 
space  were  the  fruit  of  experience :  for  experience  has  no 
element  from  which  such  truth  and  such  proof  could 
arise. 

3.  Thus  the  existence  of  necessary  truths,  such  as 
those  of  geometry,  proves  that  the  idea  of  space  from 
which  they  flow,  is  not  derived  from  experience.  Such 
truths  are  inconceivable  on  the  supposition  of  their  being 
collected  from  observation  ;  for  the  impressions  of  sense 
include  no  evidence  of  necessity.  But  we  can  readily 
understand  the  necessary  character  of  such  truths,  if  we 
conceive  that  there  are  certain  necessary  conditions  under 
which  alone  the  mind  receives  the  impressions  of  sense. 
Since  these  conditions  reside  in  the  constitution  of  the 
mind,  and  apply  to  every  perception  of  an  object  to  which 
the  mind  can  attain,  we  easily  see  that  their  rules  must 
include,  not  only  all  that  has  been,  but  all  that  can  be, 

G  2 


84  PHILOSOPHY   OF   THE   PURE   SCIENCES. 

matter  of  experience.  Our  sensations  can  each  convey 
no  information  except  about  itself;  each  can  contain  no 
trace  of  another  additional  sensation ;  and  thus  no  rela- 
tion and  connexion  between  two  sensations  can  be  given 
by  the  sensations  themselves.  But  the  mode  in  which 
the  mind  perceives  these  impressions  as  objects,  may  and 
will  introduce  necessary  relations  among  them :  and  thus 
by  conceiving  the  idea  of  space  to  be  a  condition  of  per- 
ception in  the  mind,  we  can  conceive  the  existence  of 
necessary  truths,  which  apply  to  all  perceived  objects. 

4.  If  we  consider  the  impressions  of  sense  as  the 
mere  materials  of  our  experience,   such  materials  may 
be  accumulated  in  any  quantity  and  in  any  order.     But 
if  we  suppose  that  this  matter  has  a  certain  form  given 
it,  in  the  act  of  being  accepted  by  the  mind,  we  can 
understand  how  it  is  that  these  materials  are  subject  to 
inevitable  rules ; — how  nothing  can  be  perceived  exempt 
from  the  relations  which  belong  to  such  a  form.     And 
since   there  arc    such  truths  applicable    to    our    expe- 
rience, and  arising  from  the  nature  of  space,  we  may 
thus  consider  space  as  a,  form  which  the  materials  given 
by  experience  necessarily  assume  in  the  mind;    as  an 
arrangement  derived  from  the  perceiving  mind,  and  not 
from  the  sensations  alone. 

5.  Thus  this  phrase, — that  space  is  a  form  belonging 
to  our   perceptive  power, — may  be  employed  to  express 
that  we  cannot  perceive  objects  as  in  space,  without  an 
operation  of  the  mind  as  well  as  of  the  senses — without 
active  as  well  as  passive  faculties.     This  phrase,  how- 
ever, is  not  necessary  to  the  exposition  of  our  doctrines. 
Whether  we  call  the  conception  of  space  a  condition  of 
perception,  a  form  of  perception,  or  an  idea,  or  by  any 
other  term,  it  is  something  originally  inherent  in  the  mind 
perceiving,  and  not  in  the  objects  perceived.     And  it  is 
because  the  apprehension  of  all  objects  is  thus  subjected 


OF   THE    IDEA    OF    SPACE.  85 

to  certain  mental  conditions,  forms  or  ideas,  that  our 
knowledge  involves  certain  inviolable  relations  and  neces- 
sary truths.  The  principles  of  such  truths,  so  far  as  they 
regard  space,  are  derived  from  the  idea  of  space,  and  we 
must  endeavour  to  exhibit  such  principles  in  their  general 
form.  But  before  we  do  this,  we  may  notice  some  of 
the  conditions  which  belong  not  to  our  Ideas  in  general, 
but  to  this  Idea  of  Space  in  particular. 


CHAPTER  III. 

OF  SOME  PECULIARITIES  OF  THE  IDEA  OF 
SPACE. 

1.  SOME  of  the  Ideas  which  we  shall  have  to  examine 
involve  conceptions  of  certain  relations  of  objects,  as  the 
idea  of  Cause  and  of  Likeness ;  and  may  appear  to  be 
suggested   by  experience,  enabling   us  to   abstract  this 
general  relation  from  particular  cases.     But  it  will  be 
seen  that  Space  is  not  such  a  general  conception  of  a 
relation.     For  we  do  not  speak  of  Spaces  as  we  speak  of 
Causes  and  Likenesses,  but  of  space.      And   when   we 
speak  of  spaces,  we  understand  by  the  expression,  parts 
of    one  and   the   same   identical  everywhere   extended 
Space.  We  conceive  a  universal  space ;  which  is  not  made 
up  of  these  partial  spaces  as  its  component  parts,  for  it 
would  remain    if   these  were  taken   away;    and   these 
cannot  be  conceived  without  presupposing  absolute  space. 
Absolute  space  is  essentially  one  ;   and  the  complication 
which  exists  in  it,  and  the  conception  of  various  spaces, 
depends  merely  upon  boundaries.     Space  must,  therefore, 
be,  as  we  have  said,  not  a  general  conception  abstracted 
from  particulars,  but  a  universal  mode  of  representation, 
altogether  independent  of  experience. 

2.  Space  is  infinite.     We  represent  it' to  ourselves  ps 


86  PHILOSOPHY   OF   THE   PURE    SCIENCES. 

an  infinitely  great  magnitude.  Such  an  idea  as  that  of 
Likeness  or  Cause,  is,  no  doubt,  found  in  an  infinite 
number  of  particular  cases,  and  so  far  includes  these 
cases.  But  these  ideas  do  not  include  an  infinite  number 
of  cases  as  parts  of  an  infinite  whole.  When  we  say 
that  all  bodies  and  partial  spaces  exist  in  infinite  space, 
we  use  an  expression  which  is  not  applied  in  the  same 
sense  to  any  cases  except  those  of  space  and  time. 

3.  What  is  here  said  may  appear  to  be  a  denial   of 
the  real  existence  of  space.     It  must  be  observed,  how- 
ever, that   we  do  not  deny,  but   distinctly  assert,  the 
existence  of  space  as  a  real  and  necessary  condition  of  all 
objects   perceived ;    and  that   we   not    only   allow   that 
objects  are  seen  external  to  us,  but  we  found  upon  the 
fact  of  their  being  so  seen,  our  view  of  the  nature  of 
space.     If,  however,  it  be  said  that  we  deny  the  reality 
of  space  as  an  object  or  thing,  this  is  true.     Nor  does  it 
appear  easy  to  maintain  that    space    exists  as  a  thing, 
when  it  is  considered  that  this  thing  is  infinite  in  all  its 
dimensions;  and,  moreover,   that   it  is   a  thing,   which, 
being  nothing  in  itself,  exists  only  that  other  things  may 
exist  in  it.      And  those  who  maintain  the  real  existence 
of  space,  must  also  maintain  the  real  existence  of  time  in 
the   same   sense.     Now  two  infinite  things,  thus  really 
existing,  and  yet  existing  only  as  other  things  exist  in 
them,  are  notions  so  extravagant  that  we  are  driven  to 
some  other  mode  of  explaining  the  state  of  the  matter. 

4.  Thus  space  is  not  an  object  of  which  we  perceive 
the  properties,  but  a  form  of  our  perception  ;   not  a  thing 
which  affects  our  senses,  but  an  idea  to  which  we  con- 
form   the   impressions    of  sense.     And  its  peculiarities 
appear  to  depend  upon  this,  that  it  is  not  only  a  form  of 
sensation,  but  of  intuition ;   that  in  reference  to  space, 
we  not  only  perceive  but  contemplate  objects.     We  see 
objects  in  space,   side  by  side,  exterior  to  each  other; 


PECULIARITIES   OF   THE   IDEA   OF   SPACE.  87 

space,  and  objects  in  so  far  as  they  occupy  space,  have 
parts  exterior  to  other  parts  ;  and  have  the  whole  thus 
made  up  by  the  juxtaposition  of  parts.  This  mode  of 
apprehension  belongs  only  to  the  ideas  of  space  and 
time.  Space  and  time  are  made  up  of  parts,  but  cause 
and  likeness  are  not  apprehended  as  made  up  of  parts. 
And  the  term  intuition  (in  its  rigorous  sense)  is  appli- 
cable only  to  that  mode  of  contemplation  in  which  we 
thus  look  at  objects  as  made  up  of  parts,  and  apprehend 
the  relations  of  those  parts  at  the  same  time  and  by  the 
same  act  by  which  we  apprehend  the  objects  themselves. 

5.  As  we   have    said,   space    limited  by   boundaries 
gives  rise  to  various  conceptions  which  we  have  often  to 
consider.     Thus  limited,  space  assumes  form  or  figure ; 
and  the  variety  of  conceptions  thus  brought  under  our 
notice  is  infinite.     We  have  every  possible  form  of  line, 
straight   line,    and    curve ;    and    of    curves    an   endless 
number; — circles,   parabolas,  hyperbolas,  spirals,  helices. 
We  have  plane  surfaces  of  various  shapes, — parallelograms, 
polygons,   ellipses ;    and  we  have  solid   figures, — cubes, 
cones,    cylinders,    spheres,    spheroids,    and   so    on.     All 
these  have    their  various  properties,  depending   on  the 
relations  of  their  boundaries ;  and  the  investigation  of 
their   properties    forms  the  business  of  the  science  of 
geometry. 

6.  Space  has  three  dimensions,  or  directions  in  which 
it  may  be  measured;  it  cannot  have  more  or  fewer.     The 
simplest  measurement  is  that  of  a  straight  line,  which 
has   length    alone.      A    surface   has    both    length    and 
breadth :  and  solid  space  has  length,  breadth,  and  thick- 
ness or  depth.     The  origin  of  such  a  difference  of  dimen- 
sions will  be  seen  if  we  reflect  that  each  portion  of  space 
has  a  boundary,  and  is  extended  both  in  the  direction  in 
which  its  boundary  extends,  and  also  in  a  direction  from 
its  boundary ;  for  otherwise  it  would  not  be  a  boundary, 


88  PHILOSOPHY    OF    THE   PURE   SCIENCES. 

A  point  has  no  dimensions.  A  line  has  but  one  dimen- 
sion,— the  distance  from  its  boundary,  or  its  length.  A 
plane,  bounded  by  a  straight  line,  has  the  dimension 
which  belongs  to  this  line,  and  also  has  another  dimension 
arising  from  the  distance  of  its  parts  from  this  boundary 
line ;  and  this  may  be  called  breadth.  A  solid,  bounded 
by  a  plane,  has  the  dimensions  which  this  plane  has ;  and 
has  also  a  third  dimension,  which  we  may  call  height  or 
depth,  as  we  consider  the  solid  extended  above  or  below 
the  plane ;  or  thickness,  if  we  omit  all  consideration  of  up 
and  down.  And  no  space  can  have  any  dimensions 
which  are  not  resoluble  into  these  three. 

We  may  now  proceed  to  consider  the  mode  in 
which  the  idea  of  space  is  employed  in  the  formation 
of  geometry. 


CHAPTER  TV. 

OF  THE  DEFINITIONS  AND  AXIOMS  WHICH 
RELATE  TO  SPACE. 

1.  THE  relations  of  space  have  been  apprehended 
with  peculiar  distinctness  and  clearness  from  the  very 
first  unfolding  of  man's  speculative  powers.  This  was  a 
consequence  of  the  circumstance  which  we  have  just 
noticed,  that  the  simplest  of  these  relations,  and  those  on 
which  the  others  depend,  are  seen  by  intuition.  Hence, 
as  soon  as  men  were  led  to  speculate  concerning  the 
relations  of  space,  they  assumed  just  principles,  and 
obtained  true  results.  It  is  said  that  the  science  of 
geometry  had  its  origin  in  Egypt,  before  the  dawn  of  the 
Greek  philosophy:  but  the  knowledge  of  the  early 
Egyptians  (exclusive  of  their  mythology)  appears  to  have 
been  purely  practical ;  and,  probably,  their  geometry 
consisted  only  in  some  maxims  of  land-measuring,  which 


DEFINITIONS   AND   AXIOMS   RELATING   TO   SPACE.        89 

is  what  the  term  implies.  The  Greeks  of  the  time  of 
Plato,  had,  however,  not  only  possessed  themselves  of 
many  of  the  most  remarkable  elementary  theorems  of 
the  science ;  but  had,  in  several  instances,  reached  the 
boundary  of  the  science  in  its  elementary  form ;  as  when 
they  proposed  to  themselves  the  problems  of  doubling 
the  cube  and  squaring  the  circle. 

But  the  deduction  of  these  theorems  by  a  systematic 
process,  and  the  primary  exhibition  of  the  simplest 
principles  involved  in  the  idea  of  space,  which  such  a 
deduction  requires,  did  not  take  place,  so  far  as  we  are 
aware,  till  a  period  somewhat  later.  The  Elements  of 
Geometry  of  Euclid,  in  which  this  task  was  performed,  are 
to  this  day  the  standard  work  on  the  subject :  the  author 
of  this  work  taught  mathematics  with  great  applause  at 
Alexandria,  in  the  reign  of  Ptolemy  Lagus,  about  280 
years  before  Christ.  The  principles  which  Euclid  makes 
the  basis  of  his  system  have  been  very  little  simplified 
since  his  time;  and  all  the  essays  and  controversies 
which  bear  upon  these  principles,  have  had  a  reference  to 
the  form  in  which  they  are  stated  by  him. 

2.  Definitions. — The  first  principles  of  Euclid's  geo- 
metry are,  as  the  first  principles  of  any  system  of  geo- 
metry must  be,  definitions  and  axioms  respecting  the 
various  ideal  conceptions  which  he  introduces ;  as  straight 
lines,  parallel  lines,  angles,  circles,  and  the  like.  But  it 
is  to  be  observed  that  these  definitions  and  axioms  are 
very  far  from  being  arbitrary  hypotheses  and  assumptions. 
They  have  their  origin  in  the  idea  of  space,  and  are 
merely  modes  of  exhibiting  that  idea  in  such  a  manner 
as  to  make  it  afford  grounds  of  deductive  reasoning. 
The  axioms  are  necessary  consequences  of  the  concep- 
tions respecting  which  they  are  asserted ;  and  the  defi- 
tions  are  no  less  necessary  limitations  of  conceptions ;  not 
requisite  in  order  to  arrive  at  this  or  that  consequence ; 


90  PHILOSOPHY    OF   THE   PURE   SCIENCES. 

but  necessary  in  order  that  it  may  be  possible  to  draw  any 
consequences,  and  to  establish  any  general  truths. 

For  example,  if  we  rest  the  end  of  one  straight 
staff  upon  the  middle  of  another  straight  staff,  and  move 
the  first  staff  into  various  positions,  we,  by  so  doing, 
alter  the  angles  which  the  first  staff  makes  with  the 
other  to  the  right  hand  and  to  the  left.  But  if  we 
place  the  staff  in  that  special  position  in  which  these  two 
angles  are  equal,  each  of  them  is  a  right  angle,  according 
to  Euclid;  and  this  is  the  definition  of  a  right  angle, 
except  that  Euclid  employs  the  abstract  conception  of 
straight  lines,  instead  of  speaking,  as  we  have  done,  of 
staves.  But  this  selection  of  the  case  in  which  the  two 
angles  are  equal  is  not  a  mere  act  of  caprice ;  as  it  might 
have  been  if  he  had  selected  a  case  in  which  these  angles 
are  unequal  in  any  proportion.  For  the  consequences 
which  can  be  drawn  concerning  the  cases  of  unequal 
angles,  do  not  lead  to  general  truths,  without  some  refer- 
ence to  that  peculiar  case  in  which  the  angles  are  equal : 
and  thus  it  becomes  necessary  to  single  out  and  define 
that  special  case,  marking  it  by  a  special  phrase.  And 
this  definition  not  only  gives  complete  and  distinct  know- 
ledge what  a  right  angle  is,  to  any  one  who  can  form  the 
conception  of  an  angle  in  general ;  but  also  supplies  a 
principle  from  which  all  the  properties  of  right  angles 
may  be  deduced. 

3.  Axioms. — With  regard  to  other  conceptions  also,  as 
circles,  squares,  and  the  like,  it  is  possible  to  lay  down 
definitions  which  are  a  sufficient  basis  for  our  reasoning, 
so  far  as  such  figures  are  concerned.  But,  besides  these 
definitions,  it  has  been  found  necessary  to  introduce 
certain  axioms  among  the  fundamental  principles  of  geo- 
metry. These  are  of  the  simplest  character ;  for  instance, 
that  two  straight  lines  cannot  cut  each  other  in  more  than 
one  point,  and  an  axiom  concerning  parallel  lines.  Like 


DEFINITIONS   AND   AXIOMS   RELATING   TO    SPACE.        91 

the  definitions,  these  axioms  flow  from  the  Idea  of  Space, 
and  present  that  idea  under  various  aspects.  They  are 
different  from  the  definitions ;  nor  can  the  definitions  be 
made  to  take  the  place  of  the  axioms  in  the  reasoning  by 
which  elementary  geometrical  properties  are  established. 
For  example,  the  definition  of  parallel  straight  lines  is, 
that  they  are  such  as,  however  far  continued,  can  never 
meet :  but,  in  order  to  reason  concerning  such  lines,  we 
must  further  adopt  some  axiom  respecting  them:  for 
example,  we  may  very  conveniently  take  this  axiom ;  that 
two  straight  lines  which  cut  one  another  are  not  both  of 
them  parallel  to  a  third  straight  line*.  The  definition 
and  the  axiom  are  seen  to  be  inseparably  connected  by 
our  intuition  of  the  properties  of  space ;  but  the  axiom 
cannot  be  proved  from  the  definition,  by  any  rigorous 
deductive  demonstration.  And  if  we  were  to  take  any 
other  definition  of  two  parallel  straight  lines,  (as  that 
they  are  both  perpendicular  to  a  third  straight  line,)  we 
should  still,  at  some  point  or  other  of  our  progress,  fall  in 
with  the  same  difficulty  of  demonstratively  establishing 
their  properties  without  some  further  assumption. 

4.  Thus  the  elementary  properties  of  figures,  which 
are  the  basis  of  our  geometry,  are  necessary  results  of  our 
Idea  of  Space  ;  and  are  connected  with  each  other  by  the 
nature  of  that  idea,  and  not  merely  by  our  hypotheses 
and  constructions.  Definitions  and  axioms  must  be  com- 
bined, in  order  to  express  this  idea  so  far  as  the  purposes 
of  demonstrative  reasoning  require.  These  verbal  enun- 
ciations of  the  results  of  the  idea  cannot  be  made  to 
depend  on  each  other  by  logical  consequence ;  but  have  a 
mutual  dependence  of  a  more  intimate  kind,  which  words 
cannot  fully  convey.  It  is  not  possible  to  resolve  these 
truths  into  certain  hypotheses,  of  which  all  the  rest  shall 
be  the  necessary  logical  consequence.  The  necessity  is 

*  This  axiom  is  simpler  and  more  convenient  than  that  of  Euclid. 
It  is  employed  by  the  late  Professor  Playfair  in  his  Geometry. 


02  PHILOSOPHY   OF   THE   PURE   SCIENCES. 

not  hypothetical,  but  intuitive.  The  axioms  require  not 
to  be  granted,  but  to  be  seen.  If  any  one  were  to  assent 
to  them  without  seeing  them  to  be  true,  his  assent  would 
be  of  no  avail  for  purposes  of  reasoning :  for  he  would  be 
also  unable  to  see  in  what  cases  they  might  be  applied. 
The  clear  possession  of  the  Idea  of  Space  is  the  first  requi- 
site for  all  geometrical  reasoning ;  and  this  clearness  of 
idea  may  be  tested  by  examining  whether  the  axioms 
offer  themselves  to  the  mind  as  evident. 

5.  The  necessity  of  ideas  added  to  sensations,  in  order 
to  produce  knowledge,  has  often  been  overlooked  or 
denied  in  modern  times.  The  ground  of  necessary  truth 
which  ideas  supply  being  thus  lost,  it  was  conceived  that 
there  still  remained  a  ground  of  necessity  in  definitions  ;— 
that  we  might  have  necessary  truths,  by  asserting  especi- 
ally what  the  definition  implicitly  involved  in  general.  It 
was  held,  also,  that  this  was  the  case  in  geometry : — that 
all  the  properties  of  a  circle,  for  instance,  were  implicitly 
contained  in  the  definition  of  a  circle.  That  this  alone  is 
not  the  ground  of  the  necessity  of  the  truths  which  regard 
the  circle, — that  we  could  not  in  this  way  unfold  a  defini- 
tion into  proportions,  without  possessing  an  intuition  of 
the  relations  to  which  the  definition  led, — has  already  been 
shown.  But  the  insufficiency  of  the  above  account  of  the 
grounds  of  necessary  geometrical  truth  appeared  in  ano- 
ther way  also.  It  was  found  impossible  to  lay  down  a 
system  of  definitions  out  of  which  alone  the  whole  of 
geometrical  truth  could  be  evolved.  It  was  found  that 
axioms  could  not  be  superseded.  No  definition  of  a 
straight  line  could  be  given  which  rendered  the  axiom 
concerning  straight  lines  superfluous.  And  thus  it  ap- 
peared that  the  source  of  geometrical  truths  was  not 
definition  alone ;  and  we  find  in  this  result  a  confirmation 
of  the  doctrine  which  we  are  here  urging,  that  this  source 
of  truth  is  to  be  found  in  the  form  or  conditions  of  our 
perception ; — in  the  idea  which  we  unavoidably  combine 


DEFINITIONS   AND   AXIOMS   RELATING   TO    SPACE.        93 

with  the  impressions  of  sense ; — in  the  activity,  and  not 
in  the  passivity  of  the  mind*. 

6.  This  will  appear  further  when  we  come  to  con- 
sider the  mode  in  which  we  exercise  our  observation 
upon  the  relations  of  space.  But  we  may,  in  the  first 
place,  make  a  remark  which  tends  to  show  the  connexion 
between  our  conception  of  a  straight  line,  and  the  axiom 
which  is  made  the  foundation  of  our  reasonings  concern- 
ing space.  The  axiom  is  this ; — that  two  straight  lines, 
which  have  both  their  ends  joined,  cannot  have  the 
intervening  parts  separated  so  as  to  inclose  a  space. 
The  necessity  of  this  axiom  is  of  exactly  the  same 
kind  as  the  necessity  of  the  definition  of  a  right  angle, 
of  which  we  have  already  spoken.  For  as  the  line 
standing  on  another  makes  right  angles  when  it  makes 
the  angles  on  the  two  sides  of  it  equal ;  so  a  line  is  a 
straight  line  when  it  makes  the  two  portions  of  space,  on 
the  two  sides  of  it,  similar.  And  as  there  is  only  a  single 
position  of  the  line  first  mentioned,  which  can  make  the 
angles  equal,  so  there  is  only  a  single  form  of  a  line  which 
can  make  the  spaces  near  the  line  similar  on  one  side  and 
on  the  other :  and  therefore  there  cannot  be  two  straight 
lines,  such  as  the  axiom  describes,  which,  between  the 
same  limits,  give  two  different  boundaries  to  space  thus 
separated.  And  thus  we  see  a  reason  for  the  axiom. 
Perhaps  this  view  may  be  further  elucidated  if  we  take  a 
leaf  of  paper,  double  it,  and  crease  the  folded  edge.  We 
shall  thus  obtain  a  straight  line  at  the  folded  edge ;  and 
this  line  divides  the  surface  of  the  paper,  as  it  was  origi- 
nally spread  out,  into  two  similar  spaces.  And  that  these 

*  I  formerly  stated  views  similar  to  these  in  some  "  Remarks'* 
appended  to  a  work  which  I  termed  The  Mechanical  Euclid,  pub- 
lished in  1837.  These  Remarks,  so  far  as  they  bear  upon  the  question 
here  discussed,  were  noticed  and  controverted  in  No.  135  of  the  Edin- 
burgh Review.  As  an  examination  of  the  reviewer's  objections  may 
serve  further  to  illustrate  the  subject,  I  shall  annex  to  this  chapter  an 
answer  to  the  article  to  which  I  have  referred. 


94  PHILOSOPHY   OP  THE   PURE   SCIENCES. 

spaces  are  similar  so  far  as  the  fold  which  separates  them 
is  concerned,  appears  from  this ; — that  these  two  parts 
coincide  when  the  paper  is  doubled.  And  thus  a  fold  in 
a  sheet  of  paper  at  the  same  time  illustrates  the  defini- 
tion of  a  straight  line  according  to  the  above  view,  and 
confirms  the  axiom  that  two  such  lines  cannot  enclose  a 
space. 

If  the  separation  of  the  two  parts  of  space  were  made 
by  any  other  than  a  straight  line ;  if,  for  instance,  the 
paper  were  cut  by  a  concave  line ;  then  on  turning  one  of 
the  parts  over,  it  is  easy  to  see  that  the  edge  of  one  part 
being  concave  one  way,  and  the  edge  of  the  other  part 
concave  the  other  way,  these  two  lines  might  enclose  a 
space.  And  each  of  them  would  divide  the  whole  space 
into  two  portions  which  were  not  similar ;  for  one  portion 
would  have  a  concave  edge,  and  the  other  a  convex  edge. 
Between  any  two  points  there  might  be  innumerable  lines 
drawn,  some  convex  one  way  arid  some  convex  the  other 
way ;  but  the  straight  line  is  the  line  which  is  not  convex 
either  one  way  or  the  other ;  it  is  the  single  medium 
standard  from  which  the  others  may  deviate  in  opposite 
directions. 

Such  considerations  as  these  show  sufficiently  that 
the  singleness  of  the  straight  line  which  connects  any 
two  points  is  a  result  of  our  fundamental  conceptions  of 
space.  But  yet  the  above  conceptions  of  the  similar 
form  of  the  two  parts  of  space  on  the  two  sides  of  a  line, 
and  of  the  form  of  a  line  which  is  intermediate  among 
all  other  forms,  are  of  so  vague  a  nature,  that  they  cannot 
fitly  be  made  the  basis  of  our  elementary  geometry  ;  and 
they  are  far  more  conveniently  replaced,  as  they  have 
been  in  almost  all  treatises  of  geometry,  by  the  axiom 
that  two  straight  lines  cannot  inclose  a  space. 

7.  But  we  may  remark  that  in  what  precedes  we  have 
considered  space  only  under  one  of  its  aspects : — as  a 
plane.  The  sheet  of  paper  which  we  assumed  in  order 


DEFINITIONS   AND   AXIOMS   RELATING   TO   SPACE.        95 

to  illustrate  the  nature  of  a  straight  line,  was  supposed  to 
be  perfectly  plane  or  flat :  for  otherwise,  by  folding  it,  we 
might  obtain  a  line  not  straight.  Now  this  assumption 
of  a  plane  appears  to  take  for  granted  that  very  concep- 
tion of  a  straight  line  which  the  sheet  was  employed  to 
illustrate ;  for  the  definition  of  a  plane  given  in  the  Ele- 
ments of  Geometry  is,  that  it  is  a  surface  on  which  lie 
all  straight  lines  drawn  from  one  point  of  the  surface  to 
another.  Arid  thus  the  explanation  above  given  of  the 
nature  of  a  straight  line, — that  it  divides  a  plane  space 
into  similar  portions  on  each  side, — appears  to  be  imper- 
fect or  nugatory. 

And  to  this  we  reply,  that  the  explanation  must  be 
rendered  complete  and  valid  by  deriving  the  conception 
of  a  plane  from  considerations  of  the  same  kind  as  those 
which  we  employed  for  a  straight  line.  Any  portion  of 
solid  space  may  be  divided  into  two  portions  by  surfaces 
passing  through  any  given  line  or  boundaries.  And  these 
surfaces  may  be  convex  either  on  one  side  or  on  the 
other,  and  they  admit  of  innumerable  changes  from  being 
convex  on  one  side  to  being  convex  on  the  other  in  any 
degree.  So  long  as  the  surface  is  convex  either  way,  the 
two  portions  of  space  which  it  separates  are  not  similar, 
one  having  a  convex  and  the  other  a  concave  boundary. 
But  there  is  a  certain  intermediate  position  of  the  sur- 
face in  which  the  two  portions  of  space  which  it  divides 
have  their  boundaries  exactly  similar.  In  this  position 
the  surface  is  neither  convex  nor  concave,  but  plane. 
And  thus  a  plane  surface  is  determined  by  this  condition 
of  its  being  that  single  surface  which  is  the  intermediate 
form  among  all  convex  and  concave  surfaces  by  which 
solid  space  can  be  divided,  and  of  its  separating  such 
space  into  two  portions,  of  which  the  boundaries,  though 
they  are  the  same  surface  in  two  opposite  positions,  are 
exactly  similar. 


96  PHILOSOPHY   OF   THE   PURE   SCIENCES. 

Thus  a  plane  is  the  simplest  and  most  symmetrical 
boundary  by  which  a  solid  can  be  divided ;  and  a  straight 
line  is  the  simplest  and  most  symmetrical  boundary  by 
which  a  plane  can  be  separated.  These  conceptions  are 
obtained  by  considering  the  boundaries  of  an  interminable 
space  capable  of  imaginary  division  in  every  direction. 
And  as  a  limited  space  may  be  separated  into  two  parts 
by  a  plane,  and  a  plane  again  separated  into  two  parts  by 
a  straight  line,  so  a  line  is  divided  into  two  portions  by  a 
point,  which  is  the  common  boundary  of  the  two  por- 
tions ;  the  end  of  the  one  and  the  beginning  of  the  other 
portion  having  itself  no  magnitude,  form,  or  parts. 

8.  The  geometrical  properties  of  planes  and  solids  are 
deducible  from  the  first  principles  of  the  Elements,  with- 
out any  new  axioms;  the  definition  of  a  plane  above 
quoted, — that  all  straight  lines  joining  its  points  lie  in  the 
plane, — being  a  sufficient  basis  for  all  reasoning  upon  these 
subjects.  And  thus  the  views  which  we  have  presented 
of  the  nature  of  space  being  verbally  expressed  by  means 
of  certain  definitions  and  axioms,  become  the  ground- 
work of  a  long  series  of  deductive  reasoning,  by  which 
is  established  a  very  large  and  curious  collection  of 
truths,  namely,  the  whole  science  of  elementary  plane 
and  solid  geometry. 

This  science  is  one  of  indispensable  use  and  constant 
reference  to  every  student  of  the  laws  of  nature ;  for  the 
relations  of  space  and  number  are  the  alphabet  in  which 
those  laws  are  written.  But  besides  the  interest  and  im- 
portance of  this  kind  which  geometry  possesses,  it  has  a 
great  and  peculiar  value  for  all  who  wish  to  understand 
the  foundations  of  human  knowledge,  and  the  methods 
by  which  it  is  acquired.  For  the  student  of  geometry 
acquires,  with  a  degree  of  insight  and  clearness  which  the 
unmathematical  reader  can  but  feebly  imagine,  a  convic- 
tion that  there  are  necessary  truths,  many  of  them  of  a 


DEFINITIONS   AND    AXIOMS    RELATING    TO    SPACE.         97 

very  complex  and  striking  character ;  and  that  a  few  of 
the  most  simple  and  self-evident  truths  which  it  is  pos- 
sible for  the  mind  of  man  to  apprehend,  may,  by  syste- 
matic deduction,  lead  to  the  most  remote  and  unexpected 
results. 

In  pursuing  such  philosophical  researches  as  that 
in  which  we  are  now  engaged,  it  is  of  great  advantage 
to  the  speculator  to  have  cultivated  to  some  extent  the 
study  of  geometry ;  since  by  this  study  he  may  become 
fully  aware  of  such  features  in  human  knowledge  as 
those  which  we  have  mentioned.  By  the  aid  of  the 
lesson  thus  learned  from  the  contemplation  of  geome- 
trical truths,  we  have  been  endeavouring  to  establish 
those  further  doctrines ; — that  these  truths  are  but  dif- 
ferent aspects  of  the  same  Fundamental  Idea,  and  that  the 
ground  of  the  necessity  which  these  truths  possess  reside 
in  the  Idea  from  which  they  flow,  this  Idea  not  being  a 
derivative  result  of  experience,  but  its  primary  rule. 
When  the  reader  has  obtained  a  clear  and  satisfactory 
view  of  these  doctrines,  so  far  as  they  are  applicable  to 
our  knowledge  concerning  space,  he  has,  we  may  trust, 
overcome  the  main  difficulty  which  will  occur  in  follow- 
ing the  course  of  the  speculations  now  presented  to  him. 
He  is  then  prepared  to  go  forwards  with  us ;  to  see  over 
how  wide  a  field  the  same  doctrines  are  applicable ;  and 
how  rich  and  various  a  harvest  of  knowledge  springs 
from  these  seemingly  scanty  principles. 

But  before  we  quit  the  subject  now  under  our  con- 
sideration, we  shall  endeavour  to  answer  some  objections 
which  have  been  made  to  the  views  here  presented ;  and 
shall  attempt  to  illustrate  further  the  active  powers  which 
we  have  ascribed  to  the  mind. 


VOL.  I.  H 


98  PHILOSOPHY    OF   THE   PURE   SCIENCES. 


CHAPTER  V. 

OF  SOME  OBJECTIONS  WHICH  HAVE  BEEN 

MADE  TO  THE  DOCTRINES  STATED 

IN  THE  PREVIOUS  CHAPTER*. 

THE  Edinburgh  Review,  No.  CXXXV.,  contains  a 
critique  on  a  work  termed  The  Mechanical  Euclid,  in  which 
opinions  were  delivered  to  nearly  the  same  effect  as  some 
of  those  stated  in  the  last  chapter,  and  in  Chapter  XI.  of 
the  First  Book.  Although  I  believe  that  there  are  no 
arguments  used  by  the  reviewer  to  which  the  answers  will 
not  suggest  themselves  in  the  mind  of  any  one  who  has 
read  with  attention  what  has  been  said  in  the  preceding 
chapters  (except,  perhaps,  one  or  two  remarks  which  have 
reference  to  mechanical  ideas),  it  may  serve  to  illustrate 
the  subject  if  I  reply  to  the  objections  directly,  taking 
them  as  the  reviewer  has  stated  them. 

1.  I  had  dissented  from  Stewart's  assertion  that  mathe- 
matical truth  is  hypothetical,  or  depends  upon  arbitrary 
definitions;  since  we  understand  by  an  hypothesis  a 
supposition,  not  only  which  we  may  make,  but  may  abstain 
from  making,  or  may  replace  by  a  different  supposition ; 

*  In  order  to  render  the  present  chapter  more  intelligible,  it  may 
be  proper  to  state  briefly  the  arguments  which  gave  occasion  to  the 
review.  After  noticing  Stewart's  assertions,  that  the  certainty  of 
mathematical  reasoning  arises  from  its  depending  upon  definitions,  and 
that  mathematical  truth  is  hypothetical ;  I  urged, — that  no  one  has  yet 
been  able  to  construct  a  system  of  mathematical  truths  by  the  aid  of 
definition  alone ;  that  a  definition  would  not  be  admissible  or  appli- 
cable except  it  agreed  with  a  distinct  conception  in  the  mind ;  that  the 
definitions  which  we  employ  in  mathematics  are  not  arbitrary  or  hypo- 
thetical, Lut  necessary  definitions ;  that  if  Stewart  had  taken  as  his 
examples  of  axioms  the  peculiar  geometrical  axioms,  his  assertions 
would  have  been  obviously  erroneous ;  and  that  the  real  foundation  of 
the  truths  of  mathematics  is  the  Idea  of  Space,  which  may  be  ex- 
pressed (for  purposes  of  demonstration)  partly  by  definitions  and 
partly  by  axioms. 


ANSWER   TO    OBJECTIONS.  99 

whereas  the  definitions  and  hypotheses  of  geometry  are 
necessarily  such  as  they  are,  and  cannot  be  altered  or 
excluded.  The  reviewer  (p.  84),  informs  us  that  he  under- 
stands Stewart,  when -he  speaks  of  hypotheses  and  defini- 
tions being  the  foundation  of  geometry,  to  speak  of  the 
hypothesis  that  real  objects  correspond  to  our  geometrical 
definitions.  "If  a  crystal  be  an  exact  hexahedron,  the 
geometrical  properties  of  the  hexahedron  may  be  predi- 
cated of  that  crystal."  To  this  I  reply,  that  such  hypo- 
theses as  this  are  the  grounds  of  our  applications  of  geo- 
metrical truths  to  real  objects,  but  can  in  no  way  be  said 
to  be  the  foundation  of  the  truths  themselves ;  that  I  do 
not  think  that  the  sense  which  the  reviewer  gives  was 
Stewart's  meaning ;  but  that  if  it  was,  this  view  of  the 
use  of  mathematics  does  not  at  all  affect  the  question 
which  both  he  and  I  proposed  to  discuss,  which  was, 
the  ground  of  mathematical  certainty.  I  may  add,  that 
whether  a  crystal  be  an  exact  hexahedron,  is  a  matter  of 
observation  and  measurement,  not  of  definition.  I  think 
the  reader  can  have  no  difficulty  in  seeing  how  little  my 
doctrine  is  affected  by  the  connexion  on  which  the  re- 
viewer thus  insists.  I  have  asserted  that  the  proposition 
which  affirms  the  square  on  the  diagonal  of  a  rectangle  to 
be  equal  to  the  squares  on  two  sides  does  not  rest  upon 
arbitrary  hypotheses ;  the  objector  answers,  that  the  pro- 
position that  the  square  on  the  diagonal  of  this  page  is 
equal  to  the  squares  on  the  sides,  depends  upon  the  arbi- 
trary hypothesis  that  the  page  is  a  rectangle.  Even  if 
this  fact  were  a  matter  of  arbitrary  hypothesis,  what 
could  it  have  to  do  with  the  general  geometrical  pro- 
position? How  could  a  single  fact,  observed  or  hypo- 
thetical, affect  a  universal  and  necessary  truth,  which 
would  be  equally  true  if  the  fact  were  false?  If  there 
be  nothing  arbitrary  or  hypothetical  in  geometry  till  we 
come  to  such  steps  in  its  application,  it  is  plain  that  the 

H  2 


100  PHILOSOPHY    OF    THE    PURE    SCIENCES. 

truths   themselves   are    not   hypothetical,    which  is  the 
question  for  us  to  decide. 

2.  The  reviewer  then  (p.  85,)  considers  the  doctrine 
that  axioms  as  well  as  definitions  are  the  foundations  of 
geometry ;  and  here  he  strangely  narrows  and  confuses 
the  discussion  by  making  himself  the  advocate  of  Stewart, 
instead  of  arguing  the  question  itself.  I  had  asserted 
that  some  axioms  are  necessary  as  the  foundations  of 
mathematical  reasoning,  in  addition  to  the  definitions. 
If  Stewart  did  not  intend  to  discuss  this  question,  I  had 
no  concern  with  what  he  had  said  about  axioms.  But  I 
had  every  reason  to  believe  that  this  was  the  question 
which  Stewart  did  intend  to  discuss.  I  conceive  there  is 
no  doubt  that  he  intended  to  give  an  opinion  upon  the 
grounds  of  mathematical  reasoning  in  general.  For  he 
begins  his  discussion  (Elements,  vol.  ii.,  p.  38,)  by  contesting 
Reid's  opinion  on  this  subject,  which  is  stated  generally ; 
and  he  refers  again  to  the  same  subject,  asserting  in 
general  terms,  that  the  first  principles  of  mathematics  are 
not  axioms  but  definitions.  If,  then,  afterwards,  he  made 
his  proof  narrower  than  his  assertion ; — if  having  declared 
that  no  axioms  are  necessary,  he  afterwards  limited  him- 
self to  showing  that  seven  out  of  twelve  of  Euclid's 
axioms  are  barren  truisms,  it  was  no  concern  of  mine  to 
contest  this  assertion,  which  left  my  thesis  untouched. 
I  had  asserted  that  the  proper  geometrical  axioms  (that 
two  straight  lines  cannot  inclose  a  space,  and  the  axiom 
about  parallel  lines)  are  indispensable  in  geometry. 
What  account  the  reviewer  gives  of  these  axioms  we 
shall  soon  see ;  but  if  Stewart  allowed  them  to  be  axioms 
necessary  to  geometrical  reasoning,  he  overturned  his 
own  assertion  as  to  the  foundations  of  such  reasoning ; 
and  if  he  said  nothing  decisive  about  these  axioms, 
which  are  the  points  on  which  the  battle  must  turn,  he 
left  his  assertion  altogether  unproved ;  nor  was  it  neces- 


ANSWER  TO   OBJECTIONS.  101 

sary  for  me  to  pursue  the  war  into  a  barren  and  unim- 
portant corner,  when  the  metropolis  was  surrendered. 
The  reviewer's  exultation  that  I  have  not  contested  the 
first  seven  axioms  is  an  amusing  example  of  the  self- 
complacent  zeal  of  advocacy. 

3.  But  let  us  turn  to  the  material  point :  the  proper 
geometrical  axioms.  What  is  the  reviewer's  account  of 
these?  Which  side  of  the  alternative  does  he  adopt? 
Do  they  depend  upon  the  definitions,  and  is  he  prepared 
to  show  the  dependence?  Or  are  they  superfluous,  and 
can  he  erect  the  structure  of  geometry  without  their  aid  ? 
One  of  these  two  courses,  it  would  seem,  he  must  take. 
For  we  both  begin  by  asserting  the  excellence  of  geometry 
as  an  example  of  demonstrated  truth.  It  is  precisely 
this  attribute  which  gives  an  interest  to  our  present  in- 
quiry. How,  then,  does  the  reviewer  explain  this  excel- 
lence on  his  views  ?  How  does  he  reckon  the  foundation 
courses  of  the  edifice  which  we  agree  in  considering  as  a 
perfect  example  of  intellectual  building? 

I  presume  I  may  take,  as  his  answer  to  this  question, 
his  hypothetical  statement  of  what  Stewart  would  have 
said,  (p.  87,)  on  the  supposition  that  there  had  been,  among 
the  foundations  of  geometry,  self-evident  indemonstrable 
truths :  although  it  is  certainly  strange  that  the  reviewer 
should  not  venture  to  make  up  his  mind  as  to  the  truth  or 
falsehood  of  this  supposition.  If  there  were  such  truths 
they  would  be,  he  says,  "  legitimate  filiations"  of  the  defi- 
nitions. They  would  be  involved  in  the  definitions. 
And  again  he  speaks  of  the  foundation  of  the  geo- 
metrical doctrine  of  parallels  as  a  flaw,  and  as  a  truth 
which  requires,  but  has  not  received  demonstration. 
And  yet  again,  he  tells  us  that  each  of  these  supposed 
axioms  (Euclid's  twelfth,  for  instance),  is  "merely  an 
indication  of  the  point  at  which  geometry  fails  to  perform 
that  which  it  undertakes  to  perform"  (p.  91);  and 


102  PHILOSOPHY    OF    THE    PURE    SCIENCES. 

that  in  reality  her  truths  are  not  yet  demonstrated.  The 
amount  of  this  is,  that  the  geometrical  axioms  are  to  be 
held  to  be  legitimate  filiations  of  the  definitions,  because 
though  certainly  true,  they  cannot  be  proved  from  the 
definitions ;  that  they  are  involved  in  the  definitions, 
although  they  cannot  be  evolved  out  of  them ;  and  that 
rather  than  admit  that  they  have  any  other  origin  than 
the  definitions,  we  are  to  proclaim  that  geometry  has 
failed  to  perform  what  she  undertakes  to  perform. 

To  this  I  reply  that  I  cannot  understand  what  is  meant 
by  "  legitimate  filiations  "  of  principles,  if  the  phrase  do 
not  mean  consequences  of  such  principles  established  by 
rigorous  and  formal  demonstration ;  that  the  reviewer,  if 
he  claims  any  real  signification  for  his  phrase,  must  sub- 
stantiate the  meaning  of  it  by  such  a  demonstration  ; 
he  must  establish  his  "  legitimate  filiation  "  by  a  genea- 
logical table  in  a  satisfactory  form.  When  this  cannot 
be  done,  to  assert,  notwithstanding,  that  the  propositions 
are  involved  in  the  definitions,  is  a  mere  begging  the 
question ;  and  to  excuse  this  defect  by  saying  that  geo- 
metry fails  to  perform  what  she  has  promised,  is  to  calum- 
niate the  character  of  that  science  which  we  profess  to 
make  our  standard,  rather  than  abandon  an  arbitrary 
and  unproved  assertion  respecting  the  real  grounds  of  her 
excellence.  I  add,  further,  that  if  the  doctrine  of  parallel 
lines,  or  any  other  geometrical  doctrine  of  which  we  see 
the  truth,  with  the  most  perfect  insight  of  its  necessity, 
have  not  hitherto  received  demonstration  to  the  satisfac- 
tion of  any  school  of  reasoners,  the  defect  must  arise 
from  their  erroneous  views  of  the  nature  of  demonstra- 
tions, and  the  grounds  of  mathematical  certainty. 

4,  I  conceive,  then,  that  the  reviewer  has  failed  alto- 
gether to  disprove  the  doctrine  that  the  axioms  of  geo- 
metry are  necessary  as  a  part  of  the  foundations  of  the 
science.  I  had  asserted  further  that  these  axioms  supply 


ANSWER   TO    OBJECTIONS.  103 

what  the  definitions  leave  deficient ;  and  that  they,  along 
with  definitions,  serve  to  present  the  idea  of  space  under 
such  aspects  that  we  can  reason  logically  concerning  it. 
To  this  the  reviewer  opposes  (p.  96)  the  common  opinion 
that  a  perfect  definition  is  a  complete  explanation  of  a 
name,  and  that  the  test  of  its  perfection  is,  that  we 
may  substitute  the  definition  for  the  name  wherever  it 
occurs.  I  reply,  that  my  doctrine,  that  a  definition  ex- 
presses a  part,  but  not  the  whole,  of  the  essential  cha- 
racters of  an  idea,  is  certainly  at  variance  with  an  opinion 
sometimes  maintained,  that  a  definition  merely  explains 
a  word,  and  should  explain  it  so  fully  that  it  may  always 
replace  it.  The  error  of  this  common  opinion  may,  I  think, 
be  shown  from  considerations  such  as  these ; — that  if  we 
undertake  to  explain  one  word  by  several,  we  may  be  called 
upon,  on  the  same  ground,  to  explain  each  of  these  seve- 
ral by  others,  and  that  in  this  way  we  can  reach  no  limit 
nor  resting-place :  that  in  point  of  fact,  it  is  not  found  to 
lead  to  clearness,  but  to  obscurity,  when  in  the  discussion 
of  general  principles,  we  thus  substitute  definitions  for 
single  terms ;  that  even  if  this  be  done,  we  cannot  reason 
without  conceiving  what  the  terms  mean ;  and  that,  in 
doing  this,  the  relations  of  our  conceptions,  and  not  the 
arbitrary  equivalence  of  two  forms  of  expression,  are  the 
foundations  of  our  reasoning. 

5.  The  reviewer  conceives  that  some  of  the  so-called 
axioms  are  really  definitions.  The  axiom,  that  "  magni- 
tudes which  coincide  with  each  other,  that  is,  which  fill 
the  same  space,  are  equal,"  is  a  definition  of  geometrical 
equality:  the  axiom,  that  "the  whole  is  greater  than  its 
part,"  is  a  definition  of  whole  and  part.  But  surely  there 
are  very  serious  objections  to  this  view.  It  would  seem 
more  natural  to  say,  if  the  former  axiom  is  a  definition 
of  the  word  equal,  that  the  latter  is  a  definition  of  the 
word  greater.  And  how  can  one  short,  phrase  define  two 


104  PHILOSOPHY    OF    THE    PURE    SCIENCES. 

terms  ?  If  I  say,  "  the  heat  of  summer  is  greater  than 
the  heat  of  winter,"  does  this  assertion  define  anything, 
though  the  proposition  is  perfectly  intelligible  and  dis- 
tinct? I  think,  then,  that  this  attempt  to  reduce  these 
axioms  to  definitions  is  quite  untenable. 

6.  I  have  stated  that  a  definition  can  be  of  no  use, 
except  we  can  conceive  the  possibility  and  truth  of  the 
property  connected  with  it ;  and  that  if  we  do  conceive 
this,  we  may  rightly  begin  our  reasonings  by  stating  the 
property  as  an  axiom ;  which  Euclid  does,  in  the  case  of 
straight  lines  and  of  parallels.  The  reviewer  inquires, 
(p.  92,)  whether  I  am  prepared  to  extend  this  doctrine  to 
the  case  of  circles,  for  which  the  reasoning  is  usually  rested 
upon  the  definition ;  whether  I  would  replace  this  defini- 
tion by  an  axiom,  asserting  the  possibility  of  such  a  circle. 
To  this  I  might  reply,  that  it  is  not  at  all  incumbent 
upon  me  to  assent  to  such  a  change ;  for  I  have  all  along- 
stated  that  it  is  indifferent  whether  the  fundamental  pro- 
perties from  which  we  reason  be  exhibited  as  definitions 
or  as  axioms,  provided  their  necessity  be  clearly  seen. 
But  I  am  ready  to  declare  that  I  think  the  form  of  our 
geometry  wTould  be  not  at  all  the  worse,  if,  instead  of  the 
usual  definition  of  a  circle, — "  that  it  is  a  figure  contained 
by  one  line,  which  is  called  the  circumference,  and  which 
is  such,  that  all  straight  lines  drawn  from  a  certain  point 
within  the  circumference  are  equal  to  one  another," — 
we  were  to  substitute  an  axiom  and  a  definition,  as 
follows : — 

Axiom.  If  a  line  be  drawn  so  as  to  be  at  every  point 
equally  distant  from  a  certain  point,  this  line  will  return 
into  itself,  or  will  be  one  line  including  a  space. 

Definitions.  The  space  is  called  a  circle,  the  line  the 
circumference,  and  the  point  the  centre. 

And  this  being  done,  it  would  be  true,  as  the  reviewer 
remarks,  that  geometry  cannot  stir  one  step  without 


ANSWER  TO   OBJECTIONS.  105 

resting  on  an  axiom.  And  I  do  not  at  all  hesitate  to  say, 
that  the  above  axiom,  expressed  or  understood,  is  no  less 
necessary  than  the  definition,  and  is  tacitly  assumed  in 
every  proposition  into  which  circles  enter. 

7.  I  have,  I  think,  now  disposed  of  the  principal 
objections  which  bear  upon  the  proper  axioms  of  geo- 
metry. The  principles  which  are  stated  as  the  first  seven 
axioms  of  Euclid's  Elements,  need  not,  as  I  have  said,  be 
here  discussed.  They  are  principles  which  refer,  not  to 
Space  in  particular,  but  to  Quantity  in  general :  such, 
for  instance,  as  these;  "If  equals  be  added  to  equals  the 
wholes  are  equal ;" — "  If  equals  be  taken  from  equals  the 
remainders  are  equal."  But  I  will  make  an  observation 
or  two  upon  them  before  I  proceed. 

Both  Locke  and  Stewart  have  spoken  of  these  axioms 
as  barren  truisms :  as  propositions  from  which  it  is  not 
possible  to  deduce  a  single  inference :  and  the  reviewer 
asserts  that  they  are  not  first  principles,  but  laws  of 
thought,  (p.  88.)  To  this  last  expression  I  am  willing 
to  assent ;  but  I  would  add,  that  not  only  these,  but  all 
the  principles  which  express  the  fundamental  conditions 
of  our  knowledge,  may  with  equal  propriety  be  termed 
laws  of  thought;  for  these  principles  depend  upon  our 
ideas,  and  regulate  the  active  operations  of  the  mind,  by 
which  coherence  and  connexion  are  given  to  its  passive 
impressions.  But  the  assertion  that  no  conclusions  can 
be  drawn  from  simple  axioms,  or  laws  of  human  thought 
which  regard  quantity,  is  by  no  means  true.  The  whole 
of  arithmetic, — for  instance,  the  rules  for  the  multiplica- 
tion and  division  of  large  numbers,  for  finding  a  common 
measure,  and,  in  short,  a  vast  body  of  theory  respecting 
numbers, — rests  upon  no  other  foundation  than  such 
axioms  as  have  been  just  noticed,  that  if  equals  be  added 
to  equals  the  wholes  will  be  equal.  And  even  when 
Locke's  assertion,  that  from  these  axioms  no  truths  can 


106  PHILOSOPHY    OF   THE   PURE    SCIENCES. 

be  deduced,  is  modified  by  Stewart  and  the  reviewer,  and 
limited  to  geometrical  truths,  it  is  hardly  tenable  (although, 
in  fact,  it  matters  little  to  our  argument  whether  it  is 
or  no).  For  the  greater  part  of  the  Seventh  Book  of 
Euclid's  Elements,  (on  Commensurable  and  Incommen- 
surable Quantities,)  and  the  Fifth  Book,  (on  Proportion,) 
depend  upon  these  axioms,  with  the  addition  only  of  the 
definition  or  axiom  (for  it  may  be  stated  either  way) 
which  expresses  the  idea  of  proportionality  in  numbers. 
So  that  the  attempt  to  disprove  the  necessity  and  use  of 
axioms,  as  principles  of  reasoning,  fails  even  when  we 
take  those  instances  which  the  opponents  consider  as  the 
more  manifestly  favourable  to  their  doctrine. 

8.  But  perhaps  the  question  may  have  already  sug- 
gested itself  to  the  reader's  mind,  of  what  use  can  it  be 
formally  to  state  such  principles  as  these,  (for  example, 
that  if  equals  be  added  to  equals  the  wholes  are  equal,) 
since,  whether  stated  or  no,  they  will  be  assumed  in  our 
reasoning?  And  how  can  such  principles  be  said  to  be 
necessary,  when  our  proof  proceeds  equally  well  without 
any  reference  to  them  ?  And  the  answer  is,  that  it  is 
precisely  because  these  are  the  common  principles  of 
reasoning,  which  we  naturally  employ  without  specially 
contemplating  them,  that  they  require  to  be  separated 
from  the  other  steps  and  formally  stated,  when  we 
analyse  the  demonstrations  which  we  have  obtained. 
In  every  mental  process  many  principles  are  combined 
and  abbreviated,  and  thus  in  some  measure  concealed 
and  obscured.  In  analysing  these  processes  the  combi- 
nation must  be  resolved,  and  the  abbreviation  expanded, 
and  thus  the  appearance  is  presented  of  a  pedantic  and 
superfluous  formality.  But  that  which  is  superfluous  for 
proof,  is  necessary  for  the  analysis  of  proof.  In  order  to 
exhibit  the  conditions  of  demonstration  distinctly,  they 
must  be  exhibited  formally.  In  the  same  manner,  in 


ANSWER   TO    OBJECTIONS.  107 

demonstration  we  do  not  usually  express  every  step  in 
the  form  of  a  syllogism,  but  we  see  the  grounds  of  the 
conclusiveness  of  a  demonstration,  by  resolving  it  into 
syllogisms.  Neither  axioms  nor  syllogisms  are  necessary 
for  conviction  ;  but  they  are  necessary  to  display  the  con- 
ditions under  which  conviction  becomes  inevitable.  The 
application  of  a  single  one  of  the  axioms  just  spoken  of 
is  so  minute  a  step  in  the  proof,  that  it  appears  pedantic 
to  give  it  a  marked  place ;  but  the  very  essence  of 
demonstration  consists  in  this,  that  it  is  composed  of  an 
indissoluble  succession  of  such  minute  steps.  The  admi- 
rable circumstance  is,  that  by  the  accumulation  of  such 
apparently  imperceptible  advances,  we  can  in  the  end 
make  so  vast  and  so  sure  a  progress.  The  completeness 
of  the  analysis  of  our  knowledge  appears  in  the  small- 
ness  of  the  elements  into  which  it  is  thus  resolved.  The 
minuteness  of  any  of  these  elements  of  truth,  of  axioms 
for  instance,  does  not  prevent  their  being  as  essential  as 
others  which  are  more  obvious.  And  any  attempt  to 
assume  one  kind  of  element  only  when  the  course  of  our 
analysis  brings  before  us  two  or  more  kinds,  is  alto- 
gether unphilosophical.  Axioms  and  definitions  are  the 
proximate  constituent  principles  of  our  demonstrations ; 
and  the  intimate  bond  which  connects  together  a  defini- 
tion and  an  axiom  on  the  same  subject  is  not  truly 
expressed  by  asserting  the  latter  to  be  derived  from  the 
former.  This  bond  of  connexion  exists  in  the  mind  of 
the  reasoner,  in  his  conception  of  that  to  which  both  defi- 
nition and  axiom  refer,  and  consequently  in  the  general 
Fundamental  Idea  of  which  that  conception  is  a  modifi- 
cation. 


108  PHILOSOPHY    OF    THE    PURE    SCIENCES. 

CHAPTER  VI. 
OF  THE  PERCEPTION  OF  SPACE. 

1.  ACCORDING  to  the  views  above  explained,  certain  of 
the  impressions  of  our  senses  convey  to  us  the  perception 
of  objects  as  existing  in  space ;  inasmuch  as  by  the  con- 
stitution of  our  minds  we  cannot  receive  those  impres- 
sions otherwise  than  in  a  certain  form,  involving-  such  a 
manner  of  existence.     But  the  question  deserves  to  be 
asked,  What  are  the  impressions  of  sense  by  which  we 
thus  become  acquainted  with   space  and  its  relations? 
And  as  we  have  seen  that  this  idea  of  space  implies  an 
act  of  the  mind  as  well  as  an  impression  on  the  sense, 
what  manifestations  do  we  find  of  this  activity  in  our 
observation  of  the  external  world  ? 

It  is  evident  that  sight  and  touch  are  the  senses  by 
which  the  relations  of  space  are  perceived,  principally  or 
entirely.  It  does  not  appear  that  an  odour,  or  a  feeling 
of  warmth  or  cold,  would,  independently  of  experience, 
suggest  to  us  the  conception  of  a  space  surrounding  us. 
But  when  we  see  objects,  we  see  that  they  are  extended 
and  occupy  space;  when  we  touch  them,  we  feel  that 
they  are  in  a  space  in  which  we  also  are.  We  have 
before  our  eyes  any  object,  for  instance,  a  board  covered 
with  geometrical  diagrams;  and  we  distinctly  perceive, 
by  vision,  those  lines  of  which  the  relations  are  the  sub- 
jects of  our  mathematical  reasoning.  Again,  we  see 
before  us  a  solid  object,  a  cubical  box  for  instance ;  we 
see  that  it  is  within  reach ;  we  stretch  out  the  hand  and 
perceive  by  the  touch  that  it  has  sides,  edges,  corners, 
which  we  had  already  perceived  by  vision. 

2.  Probably  most  persons  do  not  generally  apprehend 
that  there  is  any  material  difference  in  these  two  cases ; 


OF  THE  PERCEPTION  OF  SPACE.         109 

that  there  are  any  different  acts  of  mind  concerned  in 
perceiving  by  sight  a  mathematical  diagram  upon  paper, 
and  a  solid  cube  lying  on  a  table.  Yet  it  is  not  difficult 
to  show  that,  in  the  latter  case  at  least,  the  perception  of 
the  shape  of  the  object  is  not  immediate.  A  very  little 
attention  teaches  us  that  there  is  an  act  of  judgment  as 
well  as  a  mere  impression  of  sense  requisite,  in  order  that 
we  may  see  any  solid  object.  For  there  is  no  visible 
appearance  which  is  inseparably  connected  with  solidity. 
If  a  picture  of  a  cube  be  rightly  drawn  in  perspective  and 
skilfully  shaded,  the  impression  upon  the  sense  is  the  same 
as  if  it  were  a  real  cube.  The  picture  may  be  mistaken  for 
a  solid  object.  But  it  is  clear  that  in  this  case,  the  solidity 
is  given  to  the  object  by  an  act  of  mental  judgment. 
All  that  is  seen  is  outline  and  shade,  figures  and  colours 
on  a  flat  board.  The  solid  angles  and  edges,  the  relation 
of  the  faces  of  the  figure  by  which  they  form  a  cube,  is  a 
matter  of  inference.  This,  which  is  evident  in  the  case 
of  the  pictured  cube,  is  true  in  all  vision  whatever.  We 
see  a  scene  before  us  on  which  are  various  figures  and 
colours,  but  the  eye  cannot  see  more.  It  sees  length 
and  breadth,  but  no  third  dimension.  In  order  to  know 
that  there  are  solids,  we  must  infer  as  well  as  see.  And 
this  we  do  readily  and  constantly ;  so  familiarly,  indeed, 
that  we  do  not  perceive  the  operation.  Yet  we  may  detect 
this  latent  process  in  many  ways;  for  instance, by  attending 
to  cases  in  which  the  habit  of  drawing  such  inferences 
misleads  us.  Most  persons  have  experienced  this  delu- 
sion in  looking  at  a  scene  in  a  theatre,  and  especially 
that  kind  of  scene  which  is  called  a  diorama,  when 
the  interior  of  a  building  is  represented.  In  these 
cases,  the  perspective  representations  of  the  various 
members  of  the  architecture  and  decoration  impress  us 
almost  irresistibly  with  the  conviction  that  we  have 
before  us  a  space  of  great  extent  and  complex  form, 
instead  of  a  flat  painted  canvass.  Here,  at  least,  the 


110  PHILOSOPHY   OF  THE   PURE   SCIENCES. 

space  is  our  own  creation ;  but  it  is  manifestly  created 
by  the  same  act  of  thought  as  if  we  were  really  in  the 
palace  or  the  cathedral  of  which  the  halls  and  aisles  thus 
seem  to  inclose  us.  And  the  act  by  which  we  thus 
create  space  of  three  dimensions  out  of  visible  extent 
of  length  and  breadth,  is  constantly  and  imperceptibly 
going  on.  We  are  perpetually  interpreting  in  this 
manner  the  language  of  the  visible  world.  From  the 
appearances  of  things  which  we  directly  see,  we  are  con- 
stantly inferring  that  which  we  cannot  directly  see,  their 
distance  from  us,  and  the  position  of  their  parts. 

3.  The  characters  which  we  thus  interpret  are  various. 
They  are,  for  instance,  the  visible  forms,  colours,  and 
shades  of  their  parts,  understood  according  to  the  maxims 
of  perspective ;  (for  of  perspective  every  one  has  a  prac- 
tical knowledge,  as  every  one  has  of  grammar;)  the 
effort  by  which  we  fix  both  our  eyes  on  the  same  object, 
and  adjust  each  eye  to  distinct  vision;  and  the  like. 
The  right  interpretation  of  the  information  which  such 
circumstances  give  us  respecting  the  true  forms  and 
distances  of  things,  is  gradually  learned  ;  the  lesson  being 
begun  in  our  earliest  infancy,  and  inculcated  upon  us 
every  hour  during  which  we  use  our  eyes.  The  com- 
pleteness with  which  the  lesson  is  mastered  is  truly 
admirable ;  for  we  forget  that  our  conclusion  is  obtained 
indirectly,  and  mistake  a  judgment  on  evidence  for  an 
intuitive  perception.  We  see  the  breadth  of  the  street, 
as  clearly  and  readily  as  we  see  the  house  on  the  other 
side  of  it;  and  we  see  the  house  to  be  square,  however 
obliquely  it  be  presented  to  us.  This,  however,  by  no 
means  throws  any  doubt  or  difficulty  on  the  doctrine 
that  in  all  these  cases  we  do  interpret  and  infer.  The 
rapidity  of  the  process,  and  the  unconsciousness  of  the 
effort,  are  not  more  remarkable  in  this  case  than  they  are 
when  we  understand  the  meaning  of  the  speech  which 
we  hear,  or  of  the  book  which  we  read.  In  these  latter 


OF  THE  PERCEPTION  OF  SPACE.         Ill 

cases  we  merely  hear  noises  or  see  black  marks  ;  but  we 
make,  out  of  these  elements,  thought  and  feeling,  without 
being  aware  of  the  act  by  which  we  do  so.  And  by  an 
exactly  similar  process  we  see  a  variously-coloured 
expanse,  and  collect  from  it  a  space  occupied  by  solid 
objects.  In  both  cases  the  act  of  interpretation  is  become 
so  habitual  that  we  can  hardly  stop  short  at  the  mere 
impression  of  sense. 

4.  But  yet  there  are  various  ways  in  which  we  may 
satisfy  ourselves  that  these  two  parts  of  the  process  of 
seeing  objects  are  distinct.     To  separate  these  operations 
is  precisely  the   task  which  the  artist  has  to  execute  in 
making  a  drawing  of  what  he  sees.     He  has  to  recover 
the  consciousness  of  his  real  and  genuine  sen*ations,  and 
to   discern   the  lines   of  objects  as  they  appear.     This  at 
first  he  finds  difficult ;  for  he  is  tempted  to  draw  what 
he  knows  of  the  forms  of  visible  objects,  and  not  what 
he  sees :  but  as  he  improves  in  his  art,  he  learns  to  put 
on  paper  what  he  sees  only,  separate  from  what  he  infers, 
in  order  that  thus  the  inference,  and  with  it  a  conception 
like  that  of  the  reality,  may  be  left  to  the  spectator.    And 
thus  the  natural  process  of  vision  is  the  habit  of  seeing 
that  which  cannot  be  seen ;  and  the  difficulty  of  the  art 
of  drawing  consists  in  not  seeing  more  than  is  visible. 

5.  But  again ;     even   in  the   simplest    drawing   we 
exhibit  something  which  we  do  not  see.     However  slight 
is  our  representation   of  objects,  it  contains   something 
which  we  create  for  ourselves.     For  we  draw  an  outline. 
Now  an  outline  has  no  existence  in  nature.     There  are 
no  visible  lines  presented  to  the  eye  by  a  group  of  figures. 
We  separate  each  figure  from  the  rest,  and  the  boundary 
by  which  we  do  this  is  the  outline  of  the  figure  ;  and  the 
like  may  be  said  of  each  member  of  every  figure.  A  painter 
of  our  own  times  has  made  this  remark  in  a  work  upon  his 
art*.    "  The  effect  which  natural  objects  produce  upon  our 

*  PHILLIPS  on  Painting. 


112  PHILOSOPHY    OF    THE    PURE    SCIENCES. 

sense  of  vision  is  that  of  a  number  of  parts,  or  distinct 
masses  of  form  and  colour,  and  not  of  lines.  But  when 
we  endeavour  to  represent  by  painting  the  objects  which 
are  before  us,  or  which  invention  supplies  to  our  minds, 
the  first  and  the  simplest  means  we  resort  to  is  this 
picture,  by  which  we  separate  the  form  of  each  object 
from  those  that  surround  it,  marking  its  boundary,  the 
extreme  extent  of  its  dimensions  in  every  direction,  as 
impressed  on  our  vision :  and  this  is  termed  drawing  its 
outline." 

5.  Again,  there  are  other  ways  in  which  we  see  clear 
manifestations  of  the  act  of  thought  by  which  we  assign 
to  the  parts  of  objects  their  relations  in  space,  the 
impressions  of  sense  being  merely  subservient  to  this 
act.  If  we  look  at  a  medal  through  a  glass  which 
inverts  it,  we  see  the  figures  upon  it  become  concave 
depressions  instead  of  projecting  convexities;  for  the 
light  which  illuminates  the  nearer  side  of  the  convexity, 
will  be  transferred  to  the  opposite  side  by  the  apparent 
inversion  of  the  medal,  and  will  thus  imply  a  hollow 
in  which  the  side  nearest  the  light  gathers  the  shade. 
Here  our  decision  as  to  which  part  is  nearest  to  us,  has 
reference  to  the  side  from  \vhich  the  light  comes.  In 
other  cases  it  is  more  spontaneous.  If  we  draw  black 
outlines,  such  as  represent  the  edges  of  a  cube  seen 
in  perspective,  certain  of  the  lines  will  cross  each  other ; 
and  we  may  make  tins  cube  appear  to  assume  two 
different  positions,  by  determining  that  the  lines  which 
belong  to  one  end  of  the  cube  shall  be  understood  to  be 
before  or  to  be  behind  those  which  they  cross.  Here  an 
act  of  the  will,  operating  upon  the  same  sensible  image, 
gives  us  two  cubes,  occupying  two  entirely  different 
positions.  Again,  many  persons  may  have  observed  that 
when  a  windmill  in  motion  at  a  distance  from  us,  (so 
that  the  outline  of  the  sails  only  is  seen,)  stands  obliquely 
to  the  eye,  we  may,  by  an  effort  of  thought,  make  the 


OF  THE  PERCEPTION  OF  SPACE.          113 

obliquity  assume  one  or  the  other  of  two  positions ;  and 
as  we  do  this,  the  sails,  which  in  one  instance  appear  to 
turn  from  right  to  left,  in  the  other  case  turn  from  left 
to  right.  A  person  a  little  familiar  with  this  mental 
effort  can  invert  the  motion  as  often  as  he  pleases,  so 
long  as  the  conditions  of  form  and  light  do  not  offer  a 
manifest  contradiction  to  either  position. 

Thus  we  have  these  abundant  and  various  manifesta- 
tions of  the  activity  of  the  mind,  in  the  process  by  which 
we  collect  from  vision  the  relations  of  solid  space  of  three 
dimensions.  But  we  must  further  make  some  remarks  on 
the  process  by  which  we  perceive  mere  visible  figure ; 
and  also  on  the  mode  in  which  we  perceive  the  relations 
of  space  by  the  touch  ;  and  first  of  the  latter  subject. 

6.  The  opinion  above  illustrated,  that  our  sight 
does  not  give  us  a  direct  knowledge  of  the  relations  of 
solid  space,  and  that  this  knowledge  is  acquired  only  by 
an  inference  of  the  mind,  was  first  clearly  taught  by  the 
celebrated  Bishop  Berkeley*,  and  is  a  doctrine  now  gene- 
rally assented  to  by  metaphysical  speculators. 

But  does  the  sense  of  touch  give  us  directly  a  know- 
ledge of  space  ?  This  is  a  question  which  has  attracted 
considerable  notice  in  recent  times ;  and  new  light  has 
been  thrown  upon  it  in  a  degree  which  is  very  remark- 
able, when  we  consider  that  the  philosophy  of  perception 
has  been  a  prominent  subject  of  inquiry  from  the  earliest 
times.  Two  philosophers,  advancing  to  this  inquiry 
from  different  sides,  the  one  a  metaphysician,  the  other  a 
physiologist,  have  independently  arrived  at  the  conviction 
that  the  long  current  opinion,  according  to  which  we 
acquire  a  knowledge  of  space  by  the  sense  of  touch,  is 
erroneous.  And  the  doctrine  which  they  teach  instead 
of  the  ancient  error,  has  a  very  important  bearing  upon 
the  principle  which  we  are  endeavouring  to  establish, — 

*  Theory  of  Vision. 
VOL.  I.  I 


114  PHILOSOPHY    OF   THE    PURE    SCIENCES. 

that  our  knowledge  of  space  and  its  properties  is  derived 
rather  from  the  active  operations  than  from  the  passive 
impressions  of  the  percipient  mind. 

Undoubtedly  the  persuasion  that  we  acquire  a  know- 
ledge of  form  by  the  touch  is  very  obviously  suggested 
by  our  common  habits.  If  we  wish  to  know  the  form  of 
any  body  in  the  dark,  or  to  correct  the  impressions 
conveyed  by  sight,  when  we  suspect  them  to  be  false,  we 
have  only,  it  seems  to  us,  at  least  at  first,  to  stretch  forth 
the  hand  and  touch  the  object ;  and  we  learn  its  shape 
with  no  chance  of  error.  In  these  cases,  form  appears 
to  be  as  immediate  a  perception  of  the  sense  of  touch,  as 
colour  is  of  the  sense  of  sight. 

7.  But  is  this   perception  really  the    result  of  the 
passive  sense  of  touch  merely  ?     Against  such  an  opinion 
Dr.  Brown,  the  metaphysician  of  whom  I  speak,  urges* 
that  the  feeling  of  touch  alone,  when  any  object  is  applied 
to  the  hand,  or  any  other  part  of  the  body,  can  no  more 
convey  the  conception  of  form  or  extension,  than  the 
sensation  of  an  odour  or  a  taste  can  do,  except  we  have 
already  some  knowledge  of  the  relative  position  of  the 
parts  of  our  bodies ;  that  is,  except  we  are  already  in 
possession  of  an  idea  of  space,  and  have  in  our  minds 
referred  our  limbs  to  their  positions  ;  which  is  to  suppose 
the  conception  of  form  already  acquired. 

8.  By  what  faculty  then  do  we  originally  acquire  onr 
conceptions  of  the  relations  of  position  ?     Brown  answers 
by  the  muscular  sense;  that  is,  the  conscious  exertions 
of  the  various  muscles  by  which  we  move  our  limbs. 
When  we  feel  out  the  form  and  position  of  bodies  by 
the  hand,  our  knowledge  is  acquired,  not  by  the  mere 
touch  of  the  body,  but   by  perceiving  the  course  the 
fingers  must  take  in  order  to  follow  the  surface  of  the 
body,  or  to  pass  from  one  body  to  another.     We  are 

*  Lecturer,  vol.  i.  p.  450,  (J824). 


OF  THE  PERCEPTION  OF  SPACE.         115 

conscious  of  the  slightest  of  the  volitions  by  which  we 
thus  feel  out  form  and  place  ;  we  know  whether  we  move 
the  finger  to  the  right  or  left,  up  or  down,  to  us  or  from 
us,  through  a  large  or  a  small  space ;  and  all  these  con- 
scious acts  are  bound  together  and  regulated  in  our  minds 
by  an  idea  of  an  extended  space  in  which  they  are  per- 
formed. That  this  idea  of  space  is  not  borrowed  from  the 
sight,  and  transferred  to  the  muscular  feelings  by  habit, 
is  evident.  For  a  man  born  blind  can  feel  out  his  way 
with  his  staff,  and  has  his  conceptions  of  position  deter- 
mined by  the  conditions  of  space,  no  less  than  one  who 
has  the  use  of  his  eyes.  And  the  muscular  consciousness 
which  reveals  to  us  the  position  of  objects  and  parts  of 
objects  when  we  feel  them  out  by  means  of  the  hand, 
shews  itself  in  a  thousand  other  ways,  and  in  all  our 
limbs :  for  our  habits  of  standing,  walking,  and  all  other 
attitudes  and  motions,  are  regulated  by  our  feeling 
of  our  position  and  that  of  surrounding  objects.  And 
thus  we  cannot  touch  any  object  without  learning  some- 
thing respecting  its  position ;  not  that  the  sense  of  touch 
directly  conveys  such  knowledge ;  but  we  have  already 
learnt,  from  the  muscular  sense,  constantly  exercised,  the 
position  of  the  limb  which  the  object  thus  touches. 

9.  The  justice  of  this  distinction  will,  I  think,  be 
assented  to  by  all  persons  who  attend  steadily  to  the 
process  itself,  and  might  be  maintained  by  many  forcible 
reasons.  Perhaps  one  of  the  most  striking  evidences  in 
its  favour  is  that,  as  I  have  already  intimated,  it  is  the 
opinion  to  which  another  distinguished  philosopher,  Sir 
Charles  Bell,  has  been  led,  reasoning  entirely  upon  phy- 
siological principles.  From  his  researches  it  resulted  that 
besides  the  nerves  which  convey  the  impulse  of  the  will 
from  the  brain  to  the  muscle,  by  which  every  motion  of 
our  limbs  is  produced,  there  is  another  set  of  nerves  which 
carry  back  to  the  brain  a  sense  of  the  condition  of  the 

I  2 


116  PHILOSOPHY   OF   THE   PURE   SCIENCES. 

muscle,  and  thus  regulate  its  activity ;  and  give  us  the 
consciousness  of  our  position  and  relation  to  surrounding 
objects.  The  motion  of  the  hand  and  fingers,  or  the  con- 
sciousness of  this  motion,  must  be  combined  with  the 
sense  of  touch  properly  so  called,  in  order  to  make  an 
inlet  to  the  knowledge  of  such  relations.  This  conscious- 
ness of  muscular  exertion,  which  he  called  a  sixth  sense*, 
is  our  guide,  Sir  C.  Bell  shows,  in  the  common  practical 
government  of  our  motions ;  and  he  states  that  having 
given  this  explanation  of  perception  as  a  physiological 
doctrine,  he  had  with  satisfaction  seen  it  confirmed  by 
Dr.  Brown's  speculations. 

10.  Thus  it  appears  that  our  consciousness  of  the  re- 
lations of  space  is  inseparably  and  fundamentally   con- 
nected with  our  own  actions  in  space.     We  perceive  only 
while  we  act ;  our  sensations  require  to  be  interpreted  by 
our  volitions.     The  apprehension  of  extension  and  figure 
is  far  from  being  a  process  in  which  we  are  inert  and 
passive.     We  draw  lines  with  our  fingers ;  we  construct 
surfaces  by  curving  our  hands ;  we  generate  spaces  by  the 
motion  of  our  arms.     When  the  geometer  bids  us  form 
lines,  or  surfaces,  or  solids  by  motion,  he  intends  his  in- 
junction to  be  taken  as  hypothetical  only ;  we  need  only 
conceive  such  motions.     But  yet  this  hypothesis  repre- 
sents truly  the  origin  of  our  knowledge ;  we  perceive  by 
motion  at  first,  as  we  conceive  afterwards.      Or  if  not 
always  by  actual  motion,  at  least  by  potential.     If  we 
perceive  the  length  of  a  staff  by  holding  its  two  ends  in 
our  two  hands  without  running  the  finger  along  it,  this  is 
because  by  habitual  motion  we  have  already  acquired  a 
measure  of  the  distance  of  our  hands  in  any  attitude  of 
which  we  are  conscious.      Even  in  the  simplest  case,  our 
perceptions  are  derived  not  from  the  touch,  but  from  the 

*   Bridgewater   Treatise,  p.    195.      Phil.    Trans.,   1826,   p.   ii., 
p.  167. 


OF  THE  PERCEPTION  OF  SPACE.          117 

sixth  sense ;  and  this  sixth  sense  at  least,  whatever  may 
be  the  case  with  the  other  five,  implies  an  active  mind 
along  with  the  passive  sense. 

10.  Upon  attentive  consideration,  it  will  be  clear  that 
a  large  portion  of  the  perceptions  respecting  space  which 
appear  at  first  to  be  obtained  by  sight  alone,  are,  in  fact, 
acquired  by  means  of  this  sixth  sense.  Thus  we  consider 
the  visible  sky  as  a  single  surface  surrounding  us  and  re- 
turning into  itself,  and  thus  forming  a  hemisphere.  But 
such  a  mode  of  conceiving  an  object  of  vision  could  never 
have  occurred  to  us,  if  we  had  not  been  able  to  turn  our 
heads,  to  follow  this  surface,  to  pursue  it  till  we  find  it  re- 
turning into  itself.  And  when  we  have  done  this,  we 
necessarily  represent  it  to  ourselves  as  a  concave  inclosure 
within  which  we  are.  The  sense  of  sight  alone,  without 
the  power  of  muscular  motion,  could  not  have  Jed  us  to 
view  the  sky  as  a  vault  or  hemisphere.  Under  such  cir- 
cumstances, we  should  have  perceived  only  what  was  pre- 
sented to  the  eye  in  one  position;  and  if  different 
appearances  had  been  presented  in  succession,  we  could 
not  have  connected  them  as  parts  of  the  same  picture, 
for  want  of  any  perception  of  their  relative  position. 
They  would  have  been  so  many  detached  and  incohe- 
rent visual  sensations.  The  muscular  sense  connects 
their  parts  into  a  whole,  making  them  to  be  only  different 
portions  of  one  universal  scene. 

11.  These  considerations  point  out  the  fallacy  of  a  very 
curious  representation  made  by  Dr.  Reid,  of  the  convic- 
tions to  which  man  would  be  led,  if  he  possessed  vision 
without  the  sense  of  touch.  To  illustrate  this  subject, 
Reid  uses  the  fiction  of  a  nation  whom  he  terms  the  Ido- 
menians,  who  have  no  sense  except  that  of  sight.  He 
describes  their  notions  of  the  relations  of  space  as  being 
entirely  different  from  ours.  The  axioms  of  their  geome- 
try are  quite  contradictory  to  our  axioms,  For  example, 


1.18  PHILOSOPHY    OP    THE    PURE    SCIENCES. 

it  is  lield  to  be  self-evident  among  them  that  two  straight 
lines  which  intersect  each  other  once,  must  intersect  a 
second  time ;  that  the  three  angles  of  any  triangle  are 
greater  than  two  right  angles ;  and  the  like.  These  para- 
doxes are  obtained  by  tracing  the  relations  of  lines  on  the 
surface  of  a  concave  sphere,  which  surrounds  the  spec- 
tator, and  on  which  all  visible  appearances  may  be  sup- 
posed to  be  presented  to  him.  But  from  what  is  said 
above  it  appears  that  the  notion  of  such  a  sphere,  and 
such  a  connexion  of  visible  objects  which  are  seen  in  dif- 
ferent directions,  cannot  be  arrived  at  by  sight  alone. 
When  the  spectator  combines  in  his  conception  the  rela- 
tions of  long-drawn  lines  and  large  figures,  as  he  sees 
them  by  turning  his  head  to  the  right  and  to  the  left,  up- 
wards and  downwards,  he  ceases  to  be  an  Idomenian. 
And  thus  our  conceptions  of  the  properties  of  space  de- 
rived through  the  exercise  of  one  mode  of  perception  are 
not  at  variance  with  those  obtained  in  another  way ;  but 
all  such  conceptions,  however  produced  or  suggested,  are 
in  harmony  with  each  other ;  being,  as  has  already  been 
said,  only  different  aspects  of  the  same  idea. 

12.  If  our  perceptions  of  the  position  of  objects 
around  us  do  not  depend  on  the  sense  of  vision  alone,  but 
on  the  muscular  feeling  brought  into  play  when  we  turn 
our  head,  it  will  obviously  follow  that  the  same  is  true 
when  we  turn  the  eye  instead  of  the  head.  And  thus 
we  may  learn  the  form  of  objects,  not  by  looking  at 
them  with  a  fixed  gaze,  but  by  following  the  boundary  of 
them  with  the  eye.  While  the  head  is  held  perfectly 
still,  the  eye  can  rove  along  the  outlines  of  visible  objects, 
scrutinize  each  point  in  succession,  and  leap  from  one 
point  to  another ;  each  such  act  being  accompanied  by  a 
muscular  consciousness  which  makes  us  aware  of  the 
direction  in  which  the  look  is  travelling.  And  we  may 
thus  gather  information  concerning  the  figures  and  places 


OF  THE  PERCEPTION  OF  SPACE.          119 

which  we  trace  out  with  the  visual  ray,  as  the  blind 
man  learns  the  forms  of  things  which  he  traces  out  with 
his  staff,  being  conscious  of  the  motions  of  his  hand. 

13.  This  view  of  the  mode  in  which  the  eye  per- 
ceives position,  which  is  thus  supported  by  the  analogy 
of  other  members  employed  for  the  same  purpose,  is  fur- 
ther confirmed  by  Sir  Charles  Bell  by  physiological  rea- 
sons.    He  teaches  us  that*  when  an  object  is  seen  we 
employ  two  senses :  there  is  an  impression  on  the  retina ; 
but  we  receive  also  the  idea  of  position  or  relation  in 
space,  which  it  is  not  the  office  of  the  retina  to  give,  by 
our  consciousness  of  the  efforts  of  the  voluntary  muscles 
of  the  eye :  and  he  has  traced  in  detail  the  course  of  the 
nerves  by  which  these  muscles  convey  their  information. 
The  constant  searching  motion  of  the  eye,  as  he  terms  itf , 
is  the  means  by  which  we  become  aware  of  the  position 
of  objects  about  us. 

14.  It  is  not  to  our  present  purpose  to  follow  the 
physiology  of  this  subject ;  but  we  may  notice  that  Sir 
C.  Bell  has  examined  the  special  circumstances  which 
belong  to  this  operation  of  the  eye.     We  learn  from  him 
that  the  particular  point  of  the  eye  which  thus  traces  the 
forms  of  visible  objects  is  a  part  of  the  retina  which  has 
been  termed  the  sensible  spot ;  being  that  part  which  is 
most  sensible  to  the  impressions  of  light  and  colour.    This 
part,  indeed,  is  not  a  spot  of  definite  size  and  form,  for  it 
appears  that  proceeding  from  a  certain  point  of  the  retina, 
the  sensibility  diminishes  on  every  side  by  degrees.     And 
the  searching  motion  of  the   eye  arises  from  the  desire 
which  we  instinctively  feel  of  receiving  upon  the  sensible 
spot  the  image  of  the   object  to  which  the  attention  is 
directed.     We  are  uneasy  and  impatient  till  the  eye  is 
turned  so  that  this  is  effected.     And  as  our  attention   is 

*  P Idl.  Trans.,  1823.     On  the  Motions  of  the  Eye. 
t  Bridget?  aler  Treatise,  p.  282. 


120  PHILOSOPHY    OF    THE    PURE    SCIENCES. 

transferred  from  point  to  point  of  the  scene  before  us,  the 
eye,  and  this  point  of  the  eye  in  particular,  travel  along 
with  the  thoughts ;  and  the  muscular  sense  which  tells 
us  of  these  movements  of  the  organ  of  vision,  conveys 
to  us  a  knowledge  of  the  forms  and  places  which  we  thus 
successively  survey. 

15.  How  much  of  activity  there  is  in  the  process  by 
which  we  perceive  the  outlines  of  objects  appears  further 
from  the  language  by  which  we  describe  their  forms. 
We  apply  to  them  not  merely  adjectives  of  form,  but 
verbs  of  motion.  An  abrupt  hill  starts  out  of  the  plain ; 
a  beautiful  figure  has  a  gliding  outline.  We  have 

The  windy  summit,  wild  and  high, 
Roughly  rushing  on  the  sky. 

These  terms  express  the  course  of  the  eye  as  it  follows 
the  lines  by  which  such  forms  are  bounded  and  marked. 
In  like  manner  another  modern  poet*  says  of  Soracte, 

that  il  From  out  the  plain 

Heaves  like  a  long-swept  wave  about  to  break. 
And  on  the  curl  hangs  pausing. 

Thus  the  muscular  sense,  which  is  inseparably  con- 
nected with  an  act  originating  in  our  own  mind,  not  only 
gives  us  all  that  portion  of  our  perceptions  of  space  in 
which  we  use  the  sense  of  touch,  but  also,  at  least  in  a 
great  measure,  another  large  portion  of  such  perceptions, 
in  which  we  employ  the  sense  of  sight.  As  we  have 
before  seen  that  our  knowledge  of  solid  space  and  its 
properties  is  not  conceivable  in  any  other  way  than  as  the 
result  of  a  mental  act,  governed  by  conditions  depending 
on  its  own  nature ;  so  it  now  appears  that  our  perceptions 
of  visible  figure  are  not  obtained  without  an  act  performed 
under  the  same  conditions.  The  sensations  of  touch  and 
sight  are  subordinated  to  an  idea  which  is  the  basis  of 
our  speculative  knowledge  concerning  space  and  its  rela- 

*  BYRON,  Ch.  Ear.  IV.,  St.  75. 


OF  THE  PERCEPTION  OF  SPACE.         121 

tions ;  and  this  same  idea  is  disclosed  to  our  conscious- 
ness by  its  practically  regulating  our  intercourse  with  the 
external  world. 

By  considerations  such  as  have  been  adduced  and 
referred  to,  it  is  proved  beyond  doubt,  that  in  a  great 
number  of  cases  our  knowledge  of  form  and  position  is 
acquired  from  the  muscular  sense,  and  not  from  sight 
directly: — for  instance,  in  all  cases  in  which  we  have 
before  us  large  objects  and  extensive  spaces.  Whether 
in  any  case  the  eye  gives  us  a  direct  perception  of  form, 
we  shall  not  here  further  inquire.  Another  opportunity 
of  discussing  this  subject  will  occur  hereafter. 

We  now  quit  the  consideration  of  the  properties  of 
Space,  and  consider  the  Idea  of  Time. 


CHAPTER  VI. 
OF   THE    IDEA    OF    TIME. 

1.  RESPECTING  the  Idea  of  Time,  we  may  make  several 
of  the  same  remarks  which  we  made  concerning  the  idea 
of  space,  in  order  to  shew  that  it  is  not  borrowed  from 
experience ;  but  is  a  bond  of  connexion  among  the 
impressions  of  sense,  derived  from  a  peculiar  activity  of 
the  mind,  and  forming  a  foundation  both  of  our  experience 
and  of  our  speculative  knowledge. 

Time  is  not  a  notion  obtained  by  experience.  Expe- 
rience, that  is,  the  impressions  of  sense  and  our  con- 
sciousness of  our  thoughts,  gives  us  various  percep- 
tions ;  and  different  successive  perceptions  considered 
together  exemplify  the  notion  of  change.  But  this  very 
connexion  of  different  perceptions, — this  successiveness, 
— presupposes  that  the  perceptions  exist  in  time.  That 
things  happen  either  together,  or  one  after  the  other,  is 


122  PHILOSOPHY   OF   THE   PURE   SCIENCES. 

intelligible  only  by  assuming  time  as  the  condition  under 
which  they  are  presented  to  us. 

Thus  time  is  a  necessary  condition  in  the  presentation 
of  all  occurrences  to  our  minds.  We  cannot  conceive 
this  condition  to  be  taken  away.  We  can  conceive 
time  to  go  on  while  nothing  happens  in  it ;  but  we  can- 
not conceive  anything  to  happen  while  time  does  not 
go  on. 

It  is  clear  from  this  that  time  is  not  an  impression 
derived  from  experience,  in  the  same  manner  in  which 
we  derive  from  experience  our  information  concerning 
the  objects  which  exist,  and  the  occurrences  which  take 
place  in  time.  The  objects  of  experience  can  easily  be 
conceived  to  be,  or  not  to  be : — to  be  absent  as  well  as 
present.  Time  always  is,  and  always  is  present,  and 
even  in  our  thoughts  we  cannot  form  the  contrary  sup- 
position. 

2.  Thus  time  is  something  distinct  from  the  matter 
or  substance  of  our  experience,  and  may  be  considered 
as  a  necessary  form  which  that  matter  (the  experience  of 
change)  must  assume,  in  order  to  be  an  object  of  con- 
templation to  the  mind.     Time  is  one  of  the  necessary 
conditions  under  which  we  apprehend  the  information 
which  our  senses  and  consciousness  give  us.     By  con- 
sidering time  as  a  form  which  belongs  to  our  power  of 
apprehending  occurrences  and  changes,  and  under  which 
alone  all  such  experience  can  be  accepted  by  the  mind, 
we  explain  the  necessity,  which  we  find  to  exist,  of  con- 
ceiving all  such  changes  as  happening  in  time ;  and  we 
thus  see  that  time  is  not  a  property  perceived  as  existing 
in  objects,  or  as  conveyed  to  us  by  our  senses ;  but  a 
condition  impressed  upon  our  knowledge  by  the  consti- 
tution of  the  mind  itself ;  involving  an  act  of  thought  as 
well  as  an  impression  of  sense. 

3.  We  showed  that  space  is  an  idea  of  the  mind,  or 


OF   THE    PERCEPTION    OF    SPACE.  T23 

form  of  our  perceiving  power,  independent  of  experience, 
by  pointing  out  that  we  possess  necessary  and  universal 
truths  concerning  the  relations  of  space,  which  could 
never  be  given  by  means  of  experience ;  but  of  which 
the  necessity  is  readily  conceivable,  if  we  suppose  them 
to  have  for  their  basis  the  constitution  of  the  mind. 
There  exist  also  respecting  number,  many  truths  abso- 
lutely necessary,  entirely  independent  of  experience  and 
anterior  to  it ;  and  so  far  as  the  conception  of  number 
depends  upon  the  idea  of  time,  the  same  argument  might 
be  used  to  show  that  the  idea  of  time  is  not  derived  from 
experience,  but  is  a  result  of  the  native  activity  of  the 
mind:  but  we  shall  defer  all  views  of  this  kind  till  we 
come  to  the  consideration  of  Number. 

4.  Some  persons  have  supposed  that  we  obtain  the 
notion  of  time  from  the  perception  of  motion.  But  it 
is  clear  that  the  perception  of  motion,  that  is,  change  of 
place,  presupposes  the  conception  of  time,  and  is  not 
capable  of  being  presented  to  the  mind  in  any  other  way. 
If  we  contemplate  the  same  body  as  being  in  different 
places  at  different  times,  and  connect  these  observations, 
we  have  the  conception  of  motion,  which  thus  presup- 
poses the  necessary  conditions  that  existence  in  time 
implies.  And  thus  we  see  that  it  is  possible  there  should 
be  necessary  truths  concerning  all  motion,  and  conse- 
quently concerning  those  motions  which  are  the  objects  of 
experience :  but  that  the  source  of  this  necessity  is  the 
Ideas  of  time  and  space,  which,  being  universal  conditions 
of  knowledge  residing  in  the  mind,  afford  a  foundation 
for  necessary  truths. 


124  PHILOSOPHY    OF    THE    PURE   SCIENCES. 

CHAPTER  VII. 
OF  SOME  PECULIARITIES  OF  THE  IDEA  OF  TIME. 

1.  THE  Idea  of  Time,  like  the  Idea  of  Space,  offers  to 
our  notice  some  characters  which  do  not  belong  to  our 
fundamental  ideas  generally,  but  which  are  deserving  of 
remark.     These  characters  are,  in  some  respects,  closely 
similar  with  regard  to  time  and  to  space,  while,  in  other 
respects,  the  peculiarities  of  these  two  ideas  are  widely 
different.     We  shall  point  out  some  of  these   charac- 
ters. 

Time  is  not  a  general  abstract  notion  collected  from 
experience ;  as,  for  example,  a  certain  general  con- 
ception of  the  relations  of  things.  For  we  do  not  con- 
sider particular  times  as  examples  of  Time  in  general, 
(as  we  consider  particular  causes  to  be  examples  of 
Cause,)  but  we  conceive  all  particular  times  to  be  parts 
of  a  single  and  endless  Time.  This  continually-flowing 
and  endless  time  is  what  offers  itself  to  us  when  we 
contemplate  any  series  of  occurrences.  All  actual  and 
possible  times  exist  as  parts,  in  this  original  and  general 
time.  And  since  all  particular  times  are  considered  as 
derivable  from  time  in  general,  it  is  manifest  that  the 
notion  of  time  in  general  cannot  be  derived  from  the 
notions  of  particular  times.  The  notion  of  time  in  gene- 
ral is  therefore  not  a  general  conception  gathered  from 
experience. 

2.  Time  is  infinite.     Since   all  actual  and  possible 
times  exist  in  the  general  course  of  time,  this  general 
time  must  be  infinite.     All   limitation   merely  divides, 
and   does  not  terminate,   the  extent  of  absolute  time. 
Time  has  no  beginning  and  no  end ;  but  the  beginning 
and  the  end  of  every  other  existence  takes  place  in  it. 

3.  Time,  like  space,  is  not  only  a  form  of  perception 


SOME   PECULIARITIES    OF   THE   IDEA    OF  TIME.        125 

but  of  intuition.  We  contemplate  events  as  taking 
place  in  time.  We  consider  its  parts  as  added  to  one 
another,  and  events  as  filling  a  larger  or  smaller  extent 
of  such  parts.  The  time  which  any  event  takes  up  is 
the  sum  of  all  such  parts,  and  the  relation  of  the  same 
to  time  is  fully  understood  when  we  can  clearly  see  what 
portions  of  time  it  occupies,  and  what  it  does  not. 
Thus  the  relation  of  known  occurrences  to  time  is 
perceived  by  intuition ;  and  time  is  a  form  of  intuition 
of  the  external  world. 

5.  Time  is  conceived  as  a  quantity  of  one  dimension ; 
it  has  great  analogy  with  a  line,  but  none  at  all  with  a 
surface  or  solid.     Time  may  be  considered  as  consisting 
of  a  series  of  instants,  which  are  before  and  after  one 
another ;  and  they  have  no  other  relation  than  this,  of 
before  and  after.     Just  the  same  would  be  the  case  with 
a  series  of  points  taken  along  a  line ;    each  would  be 
after  those  on  one  side  of  it,  and  before  those  on  another. 
Indeed   the   analogy   between   time   and  space   of  one 
dimension  is  so  close,  that  the  same  terms  are  applied  to 
both  ideas,  and  we  hardly  know  to  which  they  originally 
belong.     Times  and  lines  are  alike  called  long  and  short; 
we  speak  of  the  beginning  and  end  of  a  line ;  of  a  point 
of  time,  and  of  the  limits  of  a  portion  of  duration. 

6.  But  as  has  been   said,  there  is  nothing  in  time 
which  corresponds  to  more  than  one  dimension  in  space, 
and  hence  nothing  which  has  any  obvious  analogy  with 
figure.     Time  resembles  a  line  indefinitely  extended  both 
ways ;  all  partial  times  are  portions  of  this  line ;  and  no 
mode  of  conceiving  time  suggests  to  us  a  line  making 
any  angle  with  the  original  line,  or  any  other  combina- 
tion which  might  give  rise  to  figures  of  any  kind.     The 
analogy  between  time  and  space,  which  in  many  circum- 
stances is  so  clear,  here  disappears  altogether.     Spaces 
of  two  and  of  three  dimensions,  planes  and  solids,  have 


126  PHILOSOPHY   OF   THE   PURE   SCIENCES. 

nothing  to  which  we  can  compare  them  in  the  concep- 
tions arising  out  of  time. 

7.  As  figure  is  a  conception  solely  appropriate  to 
space,  there  is  also  a  conception  which  peculiarly  belongs 
to  time,  namely,  the  conception  of  recurrence  of  times 
similarly  marked  ;  or,  as  it  may  be  termed,  rhythm*  using 
this  word  in  a  general  sense.  The  term  rhythm  is  most 
commonly  used  to  designate  the  recurrence  of  times 
marked  by  the  syllables  of  a  verse,  or  the  notes  of  a 
melody :  but  it  is  easy  to  see  that  the  general  conception 
of  such  a  recurrence  does  not  depend  on  the  mode  in 
which  it  is  impressed  upon  the  sense.  The  forms  of 
such  recurrence  are  innumerable.  Thus  in  such  a  line  as 

Quadrupedante  putrem  sonitii  quatit  ungula  campum, 

we  have  alternately  one  long  or  forcible  syllable,  and 
two  shorter  light  ones,  recurring  over  and  over.  In  like 
manner  in  our  own  language,  in  the  line 

At  the  close  of  tlie  day  when  the  hamlet  is  still, 

we  have  two  light  and  one  strong  syllable  repeated  four 
times  over.  Such  repetition  is  the  essence  of  versification. 
The  same  kind  of  rhythm  is  one  of  the  main  elements 
of  music,  with  this  difference  only,  that  in  music  the 
forcible  syllables  are  made  so  for  the  purposes  of  rhythm 
by  their  length  only ;  for  example,  if  either  of  the  above 
lines  were  imitated  by  a  melody  in  the  most  simple  and 
obvious  manner,  each  strong  syllable  would  occupy 
exactly  twice  as  much  time  as  two  of  the  weaker  ones. 
Something  very  analogous  to  such  rhythm  may  be  traced 
in  other  parts  of  poetry  and  art,  which  we  need  not  here 
dwell  upon.  But  in  reference  to  our  present  subject,  we 
may  remark  that  by  the  introduction  of  such  rhythm, 
the  flow  of  time,  which  appears  otherwise  so  perfectly 
simple  and  homogeneous,  admits  of  an  infinite  number  of 
varied  yet  regular  modes  of  progress.  All  the  kinds  of 
versification  which  occur  in  all  languages,  and  the  still 


SOME   PECULIARITIES   OF   THE   IDEA   OF   TIME.        127 

more  varied  forms  of  recurrence  of  notes  of  different 
lengths,  which  are  heard  in  all  the  varied  strains  of  melo- 
dies, are  only  examples  of  such  modifications,  or  configu- 
rations as  we  may  call  them,  of  time.  They  involve  re- 
lations of  various  portions  of  time,  as  figures  involve  re- 
lations of  various  portions  of  space.  But  yet  the  analogy 
between  rhythm  and  figure  is  by  no  means  very  close ; 
for  in  rhythm  we  have  relations  of  quantity  alone  in  the 
parts  of  time,  whereas  in  figure  we  have  relations  not 
only  of  quantity,  but  of  a  kind  altogether  different, — 
namely,  of  position.  On  the  other  hand,  a  repetition  of 
similar  elements,  which  does  not  necessarily  occur  in 
figures,  is  quite  essential  in  order  to  impress  upon  us  that 
measured  progress  of  time  of  which  we  here  speak. 
And  thus  the  ideas  of  time  and  space  have  each  its  pecu- 
liar and  exclusive  relations ;  position  and  figure  belong- 
ing only  to  space,  while  repetition  and  rhythm  are  appro- 
priate to  time. 

8.  One  of  the  simplest   forms  of  recurrence  is  alter- 
nation, as  when  we  have  alternate  strong  and  slight  syl- 
lables.    For  instance, — 

Awake,  arise,  or  be  for  ever  f&ll'n. 

Or  without  any  subordination,  as  when  we  reckon  num- 
bers, and  call  them  in  succession,  odd,  even,  odd,  even. 

9.  But  the  simplest  of  all  forms  of  recurrence  is  that 
which  has  no  variety; — in  which  a  series  of  units,  each 
considered  as  exactly  similar  to  the  rest,  succeed  each 
other ;  as  one,  one,  one,  and  so  on.    In  this  case,  however, 
we  are  led  to  consider  each  unit  with  reference  to  all  that 
have  preceded ;  and  thus  the  series  one,  one,  one,  and  so 
forth,  becomes  one,  two,  three,  four,  five,  and  so  on ;  a 
series  with  which  all  are  familiar,  and  which  may  be  con- 
tinued without  limit. 

We  thus  collect  from  that  repetition  of  which  time 
admits,  the  conception  of  Number. 


128  PHILOSOPHY   OF   THE    PURE    SCIENCES. 

10.  The  relations  of  position  and  figure  are  the  sub- 
ject of  the  science  of  geometry;  and  are,  as  we  have 
already  said,  traced  into  a  very  remarkable  and  extensive 
body  of  truths,  which  rests  for  its  foundations  on  axioms 
involved  in  the  Idea  of  Space.  There  is,  in  like  manner, 
a  science  of  great  complexity  and  extent,  which  has  its 
foundation  in  the  Idea  of  Time.  But  this  science,  as  it 
is  usually  pursued,  applies  only  to  the  conception  of  Num- 
ber, which  is,  as  we  have  said,  the  simplest  result  of  repe- 
tition. This  science  is  Theoretical  Arithmetic,  or  the  spe- 
culative doctrine  of  the  properties  and  relations  of  num- 
bers ;  and  we  must  say  a  few  words  concerning  the  prin- 
ciples which  it  is  requisite  to  assume  as  the  basis  of  this 
science. 


CHAPTER  VIII. 
OF  THE  AXIOMS  WHICH  RELATE  TO  NUMBER. 

1.  THE  foundations  of  our  speculative  knowledge  of 
the  relations  and  properties  of  Number,  as  of  Space,  are 
contained  in  the  mode  in  which  we  represent  to  ourselves 
the  magnitudes  which  are  the  subjects  of  our  reasonings. 
To  express  these  foundations  in  axioms  in  the  case  of 
number  is  a  matter  requiring  some  consideration,  for  the 
same  reason  as  in  the  case  of  geometry ;  that  is,  because 
these  axioms  are  principles  which  we  assume   as  true, 
without  being  aware  that  we  have  made  any  assumption  ; 
and  we  cannot,  without  careful  scrutiny,  determine  when 
we  have  stated  in  the  form  of  axioms,  all  that  is  necessary 
for  the  formation  of  the  science,  and  no  more  than  is 
necessary.     We   will,  however,    attempt   to  detect  the 
principles  which  really  must  form  the  basis  of  theoretical 
arithmetic. 

2.  Why  is  it  that  three  and  two  are  equal  to  four  and 


OF   THE   AXIOMS   WHICH    RELATE   TO    NUMBER.       129 

one  ?  Because  if  we  look  at  five  things  of  any  kind,  we 
see  that  it  is  so.  The  five  are  four  and  one ;  they  are 
also  three  and  two.  The  truth  of  our  assertion  is  in- 
volved in  our  being  able  to  conceive  the  number  five  at 
all.  We  perceive  this  truth  by  intuition,  for  we  cannot 
see,  or  imagine  we  see,  five  things,  without  perceiving 
also  that  the  assertion  above  stated  is  true. 

But  how  do  we  state  in  words  this  fundamental  prin- 
ciple of  the  doctrine  of  numbers?  Let  us  consider  a 
very  simple  case.  If  we  wish  to  show  that  seven  and 
two  are  equal  to  four  and  five,  we  say  that  seven  are  four 
and  three,  therefore  seven  and  two  are  four  and  three 
and  two ;  and  because  three  and  two  are  five,  this  is  four 
and  five.  The  axioms  by  which  mathematical  reasoners 
justify  the  first  inference  (marked  by  the  conjunctive 
word  therefore],  is  by  saying  that  "  When  equals  are  added 
to  equals  the  wholes  are  equal,"  and  that  thus,  since 
seven  is  equal  to  three  and  four,  if  we  add  two  to  both, 
seven  and  two  are  equal  to  four  and  three  and  two. 

3.  Such  axioms  as  this,  that  when  equals  are  added  to 
equals  the  wholes  are  equal,  are,  in  fact,  expressions  of 
the  general  condition  of  intuition,  by  which  a  whole  is 
contemplated  as  made  up  of  parts,  and  as  identical  with 
the  aggregate  of  the  parts.   And  a  yet  more  general  form 
in  which  we  might  more  adequately  express  this  condi- 
tion of  intuition  would  be  this  ;  that  "  Two  magnitudes 
are  equal  when  they  can  be  divided  into  parts  which  are 
equal,  each  to  each."     Thus  in  the  above  example,  seven 
and  two  are  equal  to   four   and   five,  because  each  of 
the  two  sums  can  be  divided  into  the  parts,  four,  three, 
and  two. 

4.  In  all  these  cases  a  person  who  had  never  seen 
such  axioms  enunciated  in  a  verbal  form  would  employ 
the  same  reasoning  as  a  practised  mathematician,  in  order 
to  satisfy  himself  that  the   proposition  was   true.     The 

VOL.  i.  K 


130  PHILOSOPHY   OF   THE   PURE   SCIENCES. 

steps  of  the  reasoning,  being  seen  to  be  true  by  intuition, 
would  carry  an  entire  conviction,  whether  or  not  the 
argument  were  made  verbally  complete.  Hence  the 
axioms  may  appear  superfluous,  and  on  this  account  such 
axioms  have  often  been  spoken  contemptuously  of  as 
empty  and  barren  assertions.  In  fact,  however,  although 
they  cannot  supply  the  deficiency  of  the  clear  intuition 
of  number  and  space  in  the  reasoner  himself,  and 
although  when  he  possesses  such  a  faculty,  he  will  reason 
rightly  if  he  have  never  heard  of  such  axioms,  they  still 
have  their  place  properly  at  the  beginning  of  our  trea- 
tises on  the  science  of  quantity ;  since  they  express,  as 
simply  as  words  can  express,  those  conditions  of  the 
intuition  of  magnitudes  on  which  all  reasoning  concern- 
ing quantity  must  be  based ;  and  are  necessary  when  we 
want,  not  only  to  see  the  truth  of  the  elementary  reason- 
ings on  these  subjects,  but  to  put  such  reasonings  in  a 
formal  and  logical  shape. 

5.  We  have  considered  the  axioms  which  we  have 
suggested  above  as  the  basis  of  all  arithmetical   opera- 
tions of  the   nature   of  addition.     But  it  is  easily  seen 
that  the  same  principle  may  be  carried  into  other  cases ; 
as  for  instance,  multiplication,  which  is  merely  a  repeated 
addition,    and   admits   of  the   same   kind    of    evidence. 
Thus  five  times  three  are  equal  to  three  times  five ;  why 
is  this  ?     If  we  arrange   fifteen   things  in   five  rows  of 
three,  it  is  seen  by  looking,    or  by  imaginary  looking, 
which  is  intuition,  that  they  may  also  be  taken  as  three 
rows  of  five.     And  thus  the  principle  that  those  wholes 
are  equal  which  can  be  resolved  into  the  same  partial 
magnitudes,  is  immediately  applicable  in  this  as  in  the 
other  case. 

6.  We  may  proceed  to  higher  numbers,  and  may  find 
ourselves    obliged   to    use   artificial    nomenclature    and 
notation  in  order  to  represent  and  reckon  them ;  but  the 


OF   THE   AXIOMS    WHICH    RELATE   TO    NUMBER.       131 

reasoning*  in  these  cases  also  is  still  the  same.  And  the 
usual  artifice  by  whicli  our  reasoning  in  such  instances  is 
assisted  is,  that  the  number  whicli  is  the  root  of  our  scale 
of  notation  (which  is  ten  in  our  usual  system),  is  alter- 
nately separated  into  parts  and  treated  as  a  single  thing. 
Thus  47  and  35  are  82 ;  for  47  is  four  tens  and  seven ; 
35  is  three  tens  and  five ;  whence  47  and  35  are  seven 
tens  and  twelve ;  that  is,  7  tens,  1  ten,  and  2 ;  which  is 
8  tens  and  2,  or  82.  The  like  reasoning  is  applicable  in 
other  cases.  And  since  the  most  remote  and  complex 
properties  of  numbers  are  obtained  by  a  prolongation  of 
a  course  of  reasoning  exactly  similar  to  that  by  which  we 
thus  establish  the  most  elementary  propositions,  we  have 
in  the  principles  just  noticed,  the  foundation  of  the  whole 
of  Theoretical  Arithmetic. 


CHAPTER  IX. 
OF  THE  PERCEPTION  OF  TIME  AND  NUMBER. 

1.  OUR  perception  of  the  passage  of  time  involves  a 
series  of  acts  of  memory.  This  is  easily  seen  and  assented 
to,  when  large  intervals  of  time  and  a  complex  train  of 
occurrences  are  concerned.  But  since  memory  is  requi- 
site in  order  to  apprehend  time  in  such  cases,  we  cannot 
doubt  that  the  same  faculty  must  be  concerned  in  the 
shortest  and  simplest  cases  of  succession ;  for  it  will 
hardly  be  maintained  that  the  process  by  which  we  con- 
template the  progress  of  time  is  different  when  small 
and  when  large  intervals  are  concerned.  If  memory  be 
absolutely  requisite  to  connect  two  events  which  begin 
and  end  a  day,  and  to  perceive  a  tract  of  time  between 
them,  it  must  be  equally  indispensable  to  connect  the 
beginning  and  end  of  a  minute,  or  a  second;  though  in 

K  2 


132  PHILOSOPHY   OF   THE   PURE   SCIENCES. 

this  case  the  effort  may  be  smaller,  and  consequently 
more  easily  overlooked.  In  common  cases,  we  are 
unconscious  of  the  act  of  thought  by  which  we  recollect 
the  preceding  instant,  though  we  perceive  the  effort 
when  we  recollect  some  distant  event.  And  this  is 
analogous  to  what  happens  in  other  instances.  Thus,  we 
walk  without  being  conscious  of  the  volitions  by  which 
we  move  our  muscles ;  but,  in  order  to  leap,  a  distinct 
and  manifest  exertion  of  the  same  muscles  is  necessary. 
Yet  no  one  will  doubt  that  we  walk  as  well  as  leap  by 
an  act  of  the  will  exerted  through  the  muscles ;  and  in 
like  manner  our  consciousness  of  small  as  well  as  large 
intervals  of  time  involves  something  of  the  nature  of  an 
act  of  memory. 

2.  But  this  constant  and  almost  imperceptible  kind 
of  memory,  by  which  we  connect  the  beginning  and  end 
of  each  instant  as  it  passes,  may  very  fitly  be  distinguished 
in   common   cases   from   manifest   acts    of  recollection, 
although  it  may  be  difficult  or  impossible  to  separate  the 
two  operations  in  general.     This  perpetual  and  latent 
kind  of  memory  may  be  termed  a  sense  of  successive- 
ness;   and  must  be  considered  as  an  internal  sense  by 
which  we  perceive  ourselves  existing  in  time,  much  in 
the  same  way  as   by  our  external   or  muscular   sense 
we  perceive  ourselves  existing  in  space.     And  both  our 
internal   thoughts   and   feelings,  and  the  events  which 
take  place  around  us,  are  apprehended  as  objects  of  this 
internal  sense,  and  thus  as  taking  place  in  time. 

3.  In  the  same  manner  in  which   our  interpretation 
of  the  notices  of  the  muscular  sense  implies  the  power  of 
moving  our  limbs,  and  of  touching  at  will  this  object  or 
that ;  our  apprehension  of  the  relations  of  time  by  means 
of  the  internal  sense  of  successiveness  implies  a  power  of 
recalling  what  has  past,  and  of  retaining  what  is  pass- 
ing.    We  are  able  to  seize  the  occurrences  which  have 


PERCEPTION    OF   TIME   AND    NUMBER.  133 

just  taken  place,  and  to  hold  them  fast  in  our  minds  so 
as  mentally  to  measure  their  distance  in  time  from  occur- 
rences now  present.  And  thus,  this  sense  of  successive- 
ness, like  the  muscular  sense  with  which  we  have  com- 
pared it,  implies  activity  of  the  mind  itself,  and  is  not  a 
sense  passively  receiving  impressions. 

4.  The  conception  of  Number  appears  to  require  the 
exercise  of  the  same  sense  of  succession.     At  first  sight, 
indeed,  we  seem  to  apprehend  Number  without  any  act 
of  memory,  or  any  reference  to  time :  for  example,  we 
look  at  a  horse,  and  see  that  his  legs  are  four ;  and  this 
we  seem  to  do  at  once,  without  reckoning  them.     But  it 
is  not  difficult  to  see  that  this  seeming  instantaneousness 
of  the  perception  of  small  numbers  is  an  illusion.     This 
resembles  the  many  other  cases  in  which  we  perform 
short  and  easy  acts  so  rapidly  and  familiarly  that  we  are 
unconscious  of  them ;  as  in  the  acts  of  seeing,  and  of  arti- 
culating our  words.     And  this  is  the  more  manifest,  since 
we  begin  our  acquaintance  with  number  by  counting  even 
the  smallest  numbers.     Children  and  very  rude  savages 
must  use  an  effort  to  reckon  even  their  five  fingers,  and 
find  a  difficulty  in   going  further.      And  persons  have 
been  known  who  were  able  by  habit,  or  by  a  peculiar 
natural  aptitude,  to  count  by  dozens  as  rapidly  as  common 
persons  can  by  units.     We  may  conclude,  therefore,  that 
when  we  appear  to  catch  a  small  number  by  a  single 
glance  of  the  eye,  we  do  in  fact  count  the  units  of  it  in  a 
regular,  though  very  brief  succession.     To  count  requires 
an  act  of  memory.     Of  this  we  are  sensible  when  we 
count  very  slowly,  as  when  we  reckon  the  strokes  of  a 
church  clock ;  for  in  such  a  case  we  may  forget  in  the 
intervals  of  the  strokes,  and  miscount.     Now  it  will  not 
be  doubted  that  the  nature  of  the  process  in  counting  is 
the  same  whether  we  count  fast  or  slow.     There  is  no 
definite  speed  of  reckoning  at  which  the  faculties  which 


134  PHILOSOPHY   OF   THE   PURE   SCIENCES. 

it  requires  are  changed ;  and  therefore  memory,  which  is 
requisite  in  some  cases,  must  be  so  in  all. 

The  act  of  counting,  (one,  two,  three,  and  so  on,)  is 
the  foundation  of  all  our  knowledge  of  number.  The 
intuition  of  the  relations  of  number  involves  this  act  of 
counting;  for,  as  we  have  just  seen,  the  conception  of 
number  cannot  be  obtained  in  any  other  way.  And  thus 
the  whole  of  theoretical  arithmetic  depends  upon  an  act 
of  the  mind,  and  upon  the  conditions  which  the  exercise 
of  that  act  implies.  These  have  been  already  explained 
in  the  last  chapter. 

5.  But  if  the  apprehension  of  number  be  accompanied 
by  an  act  of  the  mind,  the  apprehension  of  rhythm  is  so 
still  more  clearly.  All  the  forms  of  versification  and  the 
measures  of  melodies  are  the  creations  of  man,  who  thus 
realises  in  words  and  sounds  the  forms  of  recurrence 
which  rise  within  his  own  mind.  When  we  hear  in  a 
quiet  scene  any  rapidly-repeated  sound,  as  those  made  by 
the  hammer  of  the  smith  or  the  saw  of  the  carpenter, 
every  one  knows  how  insensibly  we  throw  these  noises 
into  a  rhythmical  form  in  our  own  apprehension.  We 
do  this  even  without  any  suggestion  from  the  sounds 
themselves.  For  instance,  if  the  beats  of  a  clock  or 
watch  be  ever  so  exactly  alike,  we  still  reckon  them 
alternately  tick-tack,  tick-tack.  That  this  is  the  case, 
may  be  proved  by  taking  a  watch  or  clock  of  such  a  con- 
struction that  the  returning  swing  of  the  pendulum  is 
silent,  and  in  which  therefore  all  the  beats  are  rigor- 
ously alike:  we  shall  find  ourselves  still  reckoning  its 
sounds  as  tick-tack.  In  this  instance  it  is  manifest  that 
the  rhythm  is  entirely  of  our  own  making.  In  melo- 
dies, also,  and  in  verses  in  which  the  rhythm  is  complex, 
obscure,  and  difficult,  we  perceive  something  is  required 
on  our  part ;  for  we  are  often  incapable  of  contributing 
our  share,  and  thus  lose  the  sense  of  the  measure  alto- 


PERCEPTION  OF  TIME   AND   NUMBER.  135 

gether.  And  when  we  consider  such  cases,  and  attend  to 
what  passes  within  us  when  we  catch  the  measure,  even 
of  the  simplest  and  best-known  air,  we  shall  no  longer 
doubt  that  an  act  of  our  own  thoughts  is  requisite  in 
such  cases,  as  well  as  impressions  on  the  sense.  And 
thus  the  conception  of  this  peculiar  modification  of  time, 
which  we  have  called  rhythm,  like  all  the  other  views 
which  we  have  taken  of  the  subject,  shows  that  we  must, 
in  order  to  form  such  conceptions,  supply  a  certain  idea 
by  our  own  thoughts,  as  well  as  merely  receive  by  senses, 
whether  external  or  internal,  the  impressions  of  appear- 
ances and  collections  of  appearances. 


CHAPTER  X. 
OF   MATHEMATICAL   REASONING. 

1.  Discursive  Reasoning. — We  have  thus  seen  that 
our  notions  of  space,  time,  and  their  modifications,  neces- 
sarily involve  a  certain  activity  of  the  mind  ;  and  that 
the  conditions  of  this  activity  form  the  foundations  of 
those  sciences  which  have  the  relations  of  space,  time, 
and  number  for  their  object.  Upon  the  fundamental 
principles  thus  established,  the  various  sciences  which 
are  included  in  the  term  Pure  Mathematics,  (Geometry, 
Algebra,  Trigonometry,  Conic  Sections  and  the  rest  of 
the  Higher  Geometry,  the  Differential  Calculus,  and  the 
like,)  are  built  up  by  a  series  of  reasonings.  These  rea- 
sonings are  subject  to  the  rules  of  logic,  as  we  have 
already  remarked ;  nor  is  it  necessary  here  to  dwell  long 
on  the  nature  and  rules  of  such  processes.  But  we  may 
here  notice  that  such  processes  are  termed  discursive,  in 
opposition  to  the  operations  by  which  we  acquire  our 
fundamental  principles,  which  are,  as  we  have  seen,  intui- 


136  PHILOSOPHY    OF   THE   PURE   SCIENCES. 

tive.  This  opposition  was  formerly  very  familiar  to  our 
writers,  as  Milton : — 

.     .     .     .     Thus  the  soul  reason  receives, 
Discursive  or  intuitive. Paradise  Lost,  v.  438. 

For  in  such  reasonings  we  obtain  our  conclusions,  not  by 
looking  at  our  conceptions  steadily  in  one  view,  which  is 
intuition,  but  by  passing  from  one  view  to  another,  like 
those  who  run  from  place  to  place  (discursus).  Thus  a 
straight  line  may  be  at  the  same  time  a  side  of  a  triangle 
and  a  radius  of  a  circle :  and  in  the  first  proposition  of 
Euclid  a  line  is  considered,  first  in  one  of  these  relations, 
and  then  in  the  other,  and  thus  the  sides  of  a  certain 
triangle  are  proved  to  be  equal.  And  by  this  "  discourse 
of  reason,"  as  by  our  older  writers  it  was  termed,  we  set 
forth  from  those  axioms  which  we  perceive  by  intuition, 
travel  securely  over  a  vast  and  varied  region,  and  become 
possessed  of  a  copious  store  of  mathematical  truths. 

2.  Technical  Terms  of  Reasoning. — The  reasoning  of 
mathematics,  thus  proceeding  from  a  few  simple  principles 
to  many  truths,  is  conducted  according  to  the  rules  of 
Logic.  If  it  be  necessary,  mathematical  proofs  may  be 
reduced  to  logical  forms,  and  expressed  in  Syllogisms, 
consisting  of  major,  minor,  and  conclusion.  But  in  most 
cases  the  syllogism  is  of  that  kind  which  is  called  by  logical 
writers  an  enthymeme ;  a  word  which  implies  something 
existing  in  the  thoughts  only,  and  which  designates  a  syl- 
logism in  which  one  of  the  premises  is  understood,  and 
not  expressed.  Thus  we  say  in  a  mathematical  proof, 
"  because  the  point  c  is  the  centre  of  the  circle  A  B,  A  c 
is  equal  to  BC;"  not  stating  the  major, — that  all  lines 
drawn  from  the  centre  of  a  circle  to  the  circumference 
are  equal ;  or  introducing  it  only  by  a  transient  reference 
to  the  definition  of  a  circle.  But  the  enthymeme  is  so 
constantly  used  in  all  habitual  forms  of  reasoning,  that  it 
does  not  occur  to  us  as  being  anything  peculiar  in  mathe- 
matical works. 


OF   MATHEMATICAL   REASONING.  137 

The  propositions  which  are  proved  to  be  generally 
true  are  termed  theorems :  but  when  anything  is  required 
to  be  done,  as  to  draw  a  line  or  a  circle  under  given  con- 
ditions, this  proposition  is  a  problem.  A  theorem  requires 
demonstration ;  a  problem,  solution.  And  for  both  pur- 
poses the  mathematician  usually  makes  a  construction. 
He  directs  us  to  draw  certain  lines,  circles,  or  other 
curves,  on  which  is  to  be  founded  his  demonstration  that 
his  theorem  is  true,  or  that  his  problem  is  solved.  Some- 
times, too,  he  establishes  some  lemma,  or  preparatory  pro- 
position, before  he  proceeds  to  his  main  task ;  and  often 
he  deduces  from  his  demonstration  some  conclusion  in 
addition  to  that  which  was  the  professed  object  of  his 
proposition ;  and  this  is  termed  a  corollary. 

These  technical  terms  are  noted  here,  not  as  being 
very  important,  but  in  order  that  they  may  not  sound 
strange  and  unintelligible  if  we  should  have  occasion  to 
use  some  of  them.  There  is,  however,  one  technical  dis- 
tinction more  peculiar,  and  more  important. 

3.  Geometrical  Analysis  and  Synthesis. — In  geome- 
trical reasoning  such  as  we  have  described,  we  introduce 
at  every  step  some  new  consideration ;  and  it  is  by  com- 
bining all  these  considerations,  that  we  arrive  at  the  con- 
clusion, that  is,  the  demonstration  of  the  proposition. 
Each  step  tends  to  the  final  result,  by  exhibiting  some 
part  of  the  figure  under  a  new  relation.  To  what  we 
have  already  proved  is  added  something  more ;  and  hence 
this  process  is  called  Synthesis,  or  putting  together.  The 
proof  flows  on,  receiving  at  every  turn  new  contributions 
from  different  quarters ;  like  a  river  fed  and  augmented 
by  many  tributary  streams.  And  each  of  these  tribu- 
taries flows  from  some  definition  or  axiom  as  its  fountain, 
or  is  itself  formed  by  the  union  of  smaller  rivulets  which 
have  sources  of  this  kind.  In  descending  along  its  course, 
the  synthetical  proof  gathers  all  these  accessions  into  one 
common  tifink,  the  proposition  finally  proved. 


138  PHILOSOPHY   OF  THE  PURE   SCIENCES. 

~  But  we  may  proceed  in  a  different  manner.  We 
may  begin  from  the  formed  river,  and  ascend  to  its 
sources.  We  may  take  the  proposition  of  which  we 
require  a. proof,  and  may  examine  what  the  supposition 
of  its  truth  implies.  If  this  be  true,  then  something  else 
may  be  seen  to  be  true ;  and  from  this,  something  else, 
and  so  on.  We  may  often  in  this  way  discover  of  what 
simpler  propositions  our  theorem  or  solution  is  com- 
pounded, and  may  resolve  these  in  succession,  till  we  come 
to  some  proposition  which  is  obvious.  This  is  geometrical 
Analysis.  Having  succeeded  in  this  analytical  process, 
we  may  invert  it;  and  may  descend  again  from  the 
simple  and  known  propositions,  to  the  proof  of  a 
theorem,  or  the  solution  of  a  problem,  which  was  our 
starting-place. 

This  process  resembles,  as  we  have  said,  tracing  a 
river  to  its  sources.  As  we  ascend  the  stream,  we  per- 
petually meet  with  bifurcations;  and  some  sagacity  is 
needed  to  enable  us  to  see  which,  in  each  case,  is  the 
main  stream:  but  if  we  proceed  in  our  research,  we 
exhaust  the  unexplored  valleys,  and  finally  obtain  a  clear 
knowledge  whence  the  waters  flow.  Analytical  is  some- 
times confounded  with  symbolical  reasoning,  on  which 
subject  we  shall  make  a  remark  in  the  next  chapter. 
The  object  of  that  chapter  is  to  notice  certain  other  fun- 
damental principles  and  ideas,  not  included  in  those 
hitherto  spoken  of,  which  we  find  thrown  in  our  way  as 
we  proceed  in  our  mathematical  speculations.  It  would 
detain  us  too  long,  and  involve  us  in  subtle  and  technical 
disquisitions,  to  examine  fully  the  grounds  of  these  prin- 
ciples ;  but  Mathematics  hold  so  important  a  place  in 
relation  to  the  inductive  sciences,  that  I  shall  briefly 
notice  the  leading  ideas  which  the  ulterior  progress  of  the 
subject  involves. 


139 


CHAPTER  XI. 

OF  THE  FOUNDATIONS  OF  THE  HIGHER 
MATHEMATICS. 

1.  The  Idea  of  a  Limit. — The  general  truths  concern- 
ing relations  of  space  which  depend  upon  the  axioms 
and  definitions  contained  in  Euclid's  Elements,  and  which 
involve  only  properties  of  straight  lines  and  circles,  are 
termed  Elementary  Geometry :  all  beyond  this  belongs  to 
the  Higher  Geometry.  To  this  latter  province  appertain, 
for  example,  all  propositions  respecting  the  lengths  of  any 
portions  of  curve  lines ;  for  these  cannot  be  obtained  by 
means  of  the  principles  of  the  Elements  alone.  Here 
then  we  must  ask  to  what  other  principles  the  geometer 
has  recourse,  and  from  what  source  these  are  drawn.  Is 
there  any  origin  of  geometrical  truth  which  we  have  not 
yet  explored  ? 

The  Idea  of  a  Limit  supplies  a  new  mode  of  establish- 
ing mathematical  truths.  Thus  with  regard  to  the  length 
of  any  portion  of  a  curve,  a  problem  which  we  have  just 
mentioned ;  a  curve  is  not  made  up  of  straight  lines,  and 
therefore  we  cannot  by  means  of  any  of  the  doctrines  of 
elementary  geometry  measure  the  length  of  any  curve. 
But  we  may  make  up  a  figure  nearly  resembling  any  curve 
by  putting  together  many  short  straight  lines,  just  as  a 
polygonal  building  of  very  many  sides  may  nearly  resemble 
a  circular  room.  And  in  order  to  approach  nearer  and 
nearer  to  the  curve,  we  may  make  the  sides  more  and 
more  small,  more  and  more  numerous.  We  may  then 
possibly-find  some  mode  of  measurement,  some  relation 
of  these  small  lines  to  other  lines,  which  is  not  disturbed 
by  the  multiplication  of  the  sides  however  far  it  be 
carried.  And  thus  we  may  do  what  is  equivalent  to 


140  PHILOSOPHY   OF   THE   PURE   SCIENCES. 

measuring  the  curve  itself;  for  by  multiplying  the  sides 
we  may  approach  more  and  more  closely  to  the  curve  till 
no  appreciable  difference  remains.  The  curve  line  is  the 
Limit  of  the  polygon ;  and  in  this  process  we  proceed  on 
the  Axiom,  that  "What  is  true  up  to  the  limit  is  true  at 
the  limit." 

This  mode  of  conceiving  mathematical  magnitudes  is 
of  wide  extent  and  use;  for  every  curve  may  be  con- 
sidered as  the  limit  of  some  polygon ;  every  varied 
magnitude,  as  the  limit  of  some  aggregate  of  simpler 
forms ;  and  thus  the  relations  of  the  elementary  figures 
enable  us  to  advance  to  the  properties  of  the  most  com- 
plex cases. 

A  Limit  is  a  peculiar  and  fundamental  conception,  the 
use  of  which  in  proving  the  propositions  of  the  Higher 
Geometry  cannot  be  superseded  by  any  combination  of 
other  hypotheses  and  definitions*.  The  axiom  just  noticed, 
that  what  is  true  up  to  the  limit  is  true  at  the  limit,  is 
involved  in  the  very  conception  of  a  limit:  and  this 
principle,  with  its  consequences,  leads  to  all  the  results 
which  form  the  subject  of  the  higher  mathematics,  whe- 
ther proved  by  the  consideration  of  evanescent  triangles, 

*  This  assertion  cannot  be  fully  proved  and  illustrated  without  a 
reference  to  mathematical  reasonings  which  would  not  be  generally 
intelligible.  I  have  shown  the  truth  of  the  assertion  in  my  Thoughts 
on  the  Study  of  Mathematics,  annexed  to  the  Principles  of  English 
University  Education.  The  proof  is  of  this  kind : — The  ultimate 
equality  of  an  arc  of  a  curve  and  the  corresponding  periphery  of  a 
polygon,  when  the  sides  of  the  polygon  are  indefinitely  increased  in 
number,  is  evident.  But  this  truth  cannot  be  proved  from  any  other 
axiom.  For  if  we  take  the  supposed  axiom,  that  a  curve  is  always 
less  than  the  including  broken  line,  this  is  not  true,  except  with  a  con- 
dition; and  in  tracing  the  import  of  this  condition,  we  find  its  neces- 
sity becomes  evident  only  when  we  introduce  a  reference  to  a  Limit. 
And  the  same  is  the  case  if  we  attempt  to  supersede  the  notion  of  a 
Limit  in  proving  any  other  simple  and  evident  proposition  in  which 
that  notion  is  involved.  Therefore  these  evident  truths  are  ^-evident, 
in  virtue  of  the  Idea  of  a  Limit. 


THE   FOUNDATION   OF   THE   HIGHER   MATHEMATICS.       141 

by  the  processes  of  the  Differential  Calculus,  or  in  any 
other  way. 

The  ancients  did  not  expressly  introduce  this  con- 
ception of  a  Limit  into  their  mathematical  reasonings; 
although   in   the    application    of   what   is   termed    the 
Method  of  Exhaustions,   (in  which  they  show  how   to 
exhaust  the  difference  between  a  polygon  and  a  curve,  or 
the  like,)  they  were  in  fact  proceeding  upon  an  obscure 
apprehension  of  principles  equivalent   to   those   of  the 
Method  of  Limits.     Yet  the  necessary  fundamental  prin- 
ciple not  having,  in  their  time,  been  clearly  developed, 
their  reasonings  were  both  needlessly  intricate  and  imper- 
fectly satisfactory.     Moreover  they  were  led  to  put  in  the 
place  of  axioms,  assumptions  which  were  by  no  means 
self-evident ;  as  when  Archimedes  assumed,  for  the  basis 
of  his  measure  of  the  circumference  of  the  circle,  the 
proposition  that  a  circular  arch  is  necessarily  less  than 
two  lines  which  inclose  it,  joining  its  extremities.     The 
reasonings  of  the  older  mathematicians,  which  professed 
to  proceed  upon  such  assumptions,  led  to  true  results 
in  reality,  only  because  they  were  guided  by  a  latent 
reference  to  the  limiting  case  of  such  assumptions.     And 
this  latent  employment  of  the  conception  of  a  Limit, 
reappeared  in  various  forms  during  the  early  period  of 
modern  mathematics ;  as  for  example,  in  the  Method  of 
Indivisibles  of  Cavalleri,  and  the  Characteristic  Triangle 
of  Barrow;  till  at  last  Newton  distinctly  referred  such 
reasonings  to  the  conception  of  a  Limit,  and  established 
the  fundamental    principles   and   processes   which   that 
conception  introduces,  with  a  distinctness  and  exactness 
which  required  little  improvement  to  make  it  as  unim- 
peachable  as   the   demonstrations    of  geometry.      And 
when  such  processes  as  Newton  thus  deduced  from  the 
conception  of  a  Limit  are  represented  by  means  of  general 
algebraical   symbols    instead    of   geometrical   diagrams, 


142  PHILOSOPHY   OF   THE   PURE   SCIENCES. 

we  have  then  before  us  the  Method  of  Fluxions,  or  the 
Differential  Calculus ;  a  mode  of  treating  mathematical 
problems  justly  considered  as  the  principal  weapon  by 
which  the  splendid  triumphs  of  modern  mathematics 
have  been  achieved. 

2.  The  Use  of  General  Symbols. — The  employment 
of  algebraical  symbols,  of  which  we  have  just  spoken, 
has  been  another  of  the  main  instruments  to  which  the 
successes  of  modern  mathematics  are  owing.  And  here 
again  the  processes  by  which  we  obtain  our  results 
depend  for  their  evidence  upon  a  fundamental  conception, 
— the  conception  of  arbitrary  symbols  as  the  Signs  of 
quantity  and  its  relations;  and  upon  a  corresponding 
axiom,  that  "  The  interpretation  of  such  symbols  must  be 
perfectly  general."  In  this  case,  as  in  the  last,  it  was 
only  by  degrees  that  mathematicians  were  led  to  a  just 
apprehension  of  the  grounds  of  their  reasoning.  For 
symbols  were  at  first  used  only  to  represent  numbers 
considered  with  regard  to  their  numerical  properties ;  and 
thus  the  science  of  algebra  was  formed.  But  it  was 
found,  even  in  cases  belonging  to  common  algebra,  that 
the  symbols  often  admitted  of  an  interpretation  which 
went  beyond  the  limits  of  the  problem,  and  which  yet 
was  not  unmeaning,  since  it  pointed  out  a  question  closely 
analogous  to  the  question  proposed.  This  was  the  case, 
for  example,  when  the  answer  was  a  negative  quantity ; 
for  when  Descartes  had  introduced  the  mode  of  repre- 
senting curves  by  means  of  algebraical  relations  among 
the  symbols  of  the  co-ordinates,  or  distances  of  each  of 
their  points  from  fixed  lines,  it  was  found  that  negative 
quantities  must  be  dealt  with  as  not  less  truly  significa* 
tive  than  positive  ones.  And  as  the  researches  of  mathe- 
maticians proceeded,  other  cases  also  were  found,  in  which 
the  symbols,  although  destitute  of  meaning  according  to 
the  original  conventions  of  their  institution,  still  pointed 


THE    FOUNDATION   OF   THE   HIGHER   MATHEMATICS.      143 

out  truths  which  could  be  verified  in  other  ways ;  as  in 
the  cases  in  which  what  are  called  impossible  quantities 
occur.  Such  processes  may  usually  be  confirmed  upon 
other  principles,  and  the  truth  in  question  may  be  esta- 
blished by  means  of  a  demonstration  in  which  no  such 
seeming  fallacies  defeat  the  reasoning.  But  it  has  also 
been  shown  in  many  such  cases,  that  the  process  in  which 
some  of  the  steps  appear  to  be  without  real  meaning, 
does  in  fact  involve  a  valid  proof  of  the  proposition. 
And  what  we  have  here  to  remark  is,  that  this  is  not 
true  accidentally  or  partially  only,  but  that  the  results  of 
systematic  symbolical  reasoning  must  always  express 
general  truths,  by  their  nature,  and  do  not,  for  their 
justification,  require  each  of  the  steps  of  the  process  to 
represent  some  definite  operation  upon  quantity.  The 
absolute  universality  of  the  interpretation  of  symbols  is  the 
fundamental  principle  of  their  use.  This  has  been  shown 
very  ably  by  Professor  Peacock  in  his  Algebra^  He  has 
there  illustrated,  in  a  variety  of  ways,  this  principle :  that 
"  If  general  symbols  express  an  identity  when  they  are 
supposed  to  be  of  any  special  nature,  they  must  also  ex- 
press an  identity  when  they  are  general  in  their  nature." 
And  thus  this  universality  of  symbols  is  a  principle  in 
addition  to  those  we  have  already  noticed ;  and  is  a  prin- 
ciple of  the  greatest  importance  in  the  formation  of 
mathematical  science,  according  to  the  wide  generality 
which  such  science  has  in  modern  times  assumed. 

3.  Connexion  of  Symbols  and  Analysis. — Since  in  our 
symbolical  reasoning  our  symbols  thus  reason  for  us,  we 
do  not  necessarily  here,  as  in  geometrical  reasoning,  go 
on  adding  carefully  one  known  truth  to  another,  till  we 
reach  the  desired  result.  On  the  contrary,  if  we  have  a 
theorem  to  prove  or  a  problem  to  solve  which  can  be 
brought  under  the  domain  of  our  symbols,  we  may  at 
once  state  the  given  but  unproved  truth,  or  the  given 


144  PHILOSOPHY    OF   THE   PURE   SCIENCES. 

combination  of  unknown  quantities,  in  its  symbolical 
form.  After  this  first  process  we  may  then  proceed  to 
trace,  by  means  of  our  symbols,  what  other  truth  is 
involved  in  the  one  thus  stated,  or  what  the  unknown 
symbols  must  signify;  resolving  step  by  step  the  symbolical 
assertion  with  which  we  began,  into  others  more  fitted  for 
our  purpose.  The  former  process  is  a  kind  of  synthesis, 
the  latter  is  termed  analysis.  And  although  symbolical 
reasoning  does  not  necessarily  imply  such  analysis ;  yet 
the  connexion  is  so  familiar,  that  the  term  analysis  is 
frequently  used  to  designate  symbolical  reasoning. 


CHAPTER  XII. 
THE  DOCTRINE  OF  MOTION. 

1.  Pure  Mechanism. — THE  doctrine  of  Motion,  of 
which  we  have  here  to  speak,  is  that  in  which  motion  is 
considered  quite  independently  of  its  cause,  force;  for 
all  consideration  of  force  belongs  to  a  class  of  ideas  en- 
tirely different  from  those  with  which  we  are  here  con- 
cerned. In  this  view  it  may  be  termed  the  pure  doctrine 
of  motion,  since  it  has  to  do  solely  with  space  and  time, 
which  are  the  subjects  of  pure  mathematics.  Although 
the  doctrine  of  motion  in  connexion  with  force,  which  is 
the  subject  of  mechanics,  is  by  far  the  most  important 
form  in  which  the  consideration  of  motion  enters  into 
the  formation  of  our  sciences,  the  pure  doctrine  of  mo- 
tion, which  treats  of  space,  time,  and  velocity,  might  be 
followed  out  so  as  to  give  rise  to  a  very  considerable  and 
curious  body  of  science.  Such  a  science  is  the  science 
of  Mechanism,  independent  of  Force,  and  considered  as 
the  solution  of  a  problem  which  may  be  thus  enunciated : 
"  To  communicate  any  given  motion  from  a  first  mover  to 


THE   DOCTRINE    OF    MOTION.  145 

a  given  body."  The  science  which  should  have  for  its 
object  to  solve  all  the  various  cases  into  which  this  pro- 
blem would  ramify,  might  be  termed  Pure  Mechanism  in 
contradistinction  to  Mechanics  Proper,  or  Machinery,  in 
which  Force  is  taken  into  consideration.  The  greater 
part  of  the  machines  which  have  been  constructed  for 
use  in  manufactures  have  been  practical  solutions  of  some 
of  the  cases  of  this  problem.  We  have  also  important 
contributions  to  such  a  science  in  the  works  of  mathe- 
maticians ;  for  example,  the  various  investigations  and 
demonstrations  which  have  been  published  respecting 
the  form  of  the  Teeth  of  Wheels,  and  Mr.  Babbage's 
memoir*  on  the  Language  of  Machinery.  There  are 
also  several  works  which  contain  collections  of  the 
mechanical  contrivances  which  have  been  invented  for 
the  purpose  of  transmitting  and  modifying  motion,  and 
these  works  may  be  considered  as  treatises  on  the  science 
of  Pure  Mechanism.  But  this  science  has  not  yet  been 
reduced  to  the  systematic  simplicity  which  is  desirable, 
nor  indeed  generally  recognised  as  a  separate  science.  It 
has  been  confounded,  under  the  common  name  of  Mecha- 
nics, with  the  other  science,  Mechanics  Proper,  or  Ma- 
chinery, which  considers  the  effect  of  force  transmitted 
by  mechanism  from  one  part  of  a  material  combination  to 
another.  For  example,  the  Mechanical  Powers,  as  they 
are  usually  termed,  (the  Lever,  the  Wheel  and  Axle,  the 
Inclined  Plane,  the  Wedge,  and  the  Screw,)  have  almost 
always  been  treated  with  reference  to  the  relation  be- 
tween the  Power  and  the  Weight,  and  not  primarily  as  a 
mode  of  changing  the  velocity  and  kind  of  the  motion. 
The  science  of  pure  motion  has  not  generally  been  sepa- 
rated from  the  science  of  motion  viewed  with  reference 
to  its  causes. 

*  On  a  Method  of  expressing  by  Signs  the  Action  of  Machinery. 
Phil.  Trans.,  1826,  p.  250. 

VOL.    I.  L 


146  PHILOSOPHY   OF   THE   PURE   SCIENCES. 

Recently,  indeed,  the  necessity  of  such  a  separation 
has  been  seen  by  those  who  have  taken  a  philosophical 
view  of  science.  Thus  this  necessity  has  been  urged  by 
M.  Ampere,  in  his  Essai  sur  la  Philosophic  des  Sciences 
(1834) :  "  Long,"  he  says,  (p.  50),  "  before  I  employed 
myself  upon  the  present  work,  I  had  remarked  that  it  is 
usual  to  omit,  in  the  beginning  of  all  books  treating  of 
sciences  which  regard  motion  and  force,  certain  conside- 
rations which,  duly  developed,  must  constitute  a  special 
science :  of  which  science  certain  parts  have  been  treated 
of,  either  in  memoirs  or  in  special  works ;  such,  for  exam- 
ple, as  that  of  Carnot  upon  Motion  considered  geometri- 
cally, and  the  essay  of  Lanz  and  Betancourt  upon  the 
Composition  of  Machines."  He  then  proceeds  to  describe 
this  science  nearly  as  we  have  done,  and  proposes  to  term 
it  Kinematics  (Cinematique),  from  Kivrjiia,  motion. 

2.  Formal  Astronomy. — I  shall  not  attempt  here  fur- 
ther to  develop  the  form  which  such  a  science  must 
assume.  But  I  may  notice  one  very  large  province  which 
belongs  to  it.  When  men  had  ascertained  the  apparent 
motions  of  the  sun,  moon,  and  stars,  to  a  moderate  de- 
gree of  regularity  and  accuracy,  they  tried  to  conceive  in 
their  minds  some  mechanism  by  which  these  motions 
might  be  produced ;  and  thus  they  in  fact  proposed  to 
themselves  a  very  extensive  problem  in  Kinematics.  This, 
indeed^  was  the  view  originally  entertained  of  the  nature 
of  the  science  of  astronomy.  Thus  Plato  in  the  seventh 
Book  of  his  Republic*,  speaks  of  astronomy  as  the 
doctrine  of  the  motion  of  solids,  meaning  thereby,  spheres. 
And  the  same  was  a  proper  description  of  the  science 
till  the  time  of  Kepler,  and  even  later :  for  Kepler 
endeavoured,  though  in  vain,  to  conjoin  with  the  know- 
ledge of  the  motions  of  the  heavenly  bodies,  those  true 
mechanical  conceptions  which  converted  formal  into 
physical  astronomy  f . 

*  P.  528.  t  Hist.  Ind.  8c.,  ii.  130. 


THE    DOCTRINE   OF    MOTION.  147 

The  astronomy  of  the  ancients  admitted  none  but 
uniform  circular  motions,  and  could  therefore  be  com- 
pletely cultivated  by  the  aid  of  their  elementary  geo- 
metry. But  the  pure  science  of  motion  might  be  extended 
to  all  motions,  however  varied  as  to  the  speed  or  the  path 
of  the  moving  body.  In  this  form  it  must  depend  upon 
the  doctrine  of  limits ;  and  the  fundamental  principle  of 
its  reasonings  would  be  this :  That  velocity  is  measured 
by  the  Limit  of  the  space  described,  considered  with 
reference  to  the  times  in  which  it  is  described.  I  shall 
not  further  pursue  this  subject ;  and  in  order  to  complete 
what  I  have  to  say  respecting  the  Pure  Sciences,  I  have 
only  a  few  words  to  add  respecting  their  bearing  on 
Inductive  Science  in  general. 


CHAPTER  XIII. 

OF  THE  APPLICATION  OF   MATHEMATICS  TO 
THE  INDUCTIVE  SCIENCES. 

1.  ALL  objects  in  the  world  which  can  be  made  the 
subjects  of  our  contemplation  are  subordinate  to  the  con- 
ditions of  Space,  Time,  and  Number ;  and  on  this  account 
the  doctrines  of  pure  mathematics  have  most  numerous 
and  extensive  applications  in  every  department  of  our 
investigations  of  nature.  And  there  is  a  peculiarity  in 
these  Ideas,  which  has  caused  the  mathematical  sciences 
to  be,  in  all  cases,  the  first  successful  efforts  of  the  awak- 
ening speculative  powers  of  nations  at  the  commence- 
ment of  their  intellectual  progress.  Conceptions  derived 
from  these  Ideas  are  from  the  very  first  perfectly  precise 
and  clear,  so  as  to  be  fit  elements  of  scientific  truths. 
This  is  not  the  case  with  the  other  conceptions  which 
form  the  subjects  of  scientific  inquiries.  The  conception 

L  2 


148  PHILOSOPHY   OF   THE    PURE   SCIENCES. 

of  statical  force,  for  instance,  was  never  presented  in  a 
distinct  form  till  the  works  of  Archimedes  appeared 
the  conception  of  accelerating  force  was  confused,  in  the 
mind  of  Kepler  and  his  contemporaries,  and  only  became 
clear  enough  for  purposes  of  sound  scientific  reasoning 
in  the  succeeding  century :  the  just  conception  of  che- 
mical composition  of  elements  gradually,  in  modern  times, 
emerged  from  the  erroneous  and  vague  notions  of  the 
ancients.  If  we  take  works  published  on  such  subjects 
before  the  epoch  when  the  foundations  of  the  true  science 
were  laid,  we  find  the  knowledge  not  only  small,  but 
worthless.  The  writers  did  not  see  any  evidence  in  what 
we  now  consider  as  the  axioms  of  the  science ;  nor  any 
inconsistency  where  we  now  see  self-contradiction.  But 
this  was  never  the  case  with  speculations  concerning 
space  and  number.  From  their  first  rise,  these  were 
true  as  far  as  they  went.  The  Geometry  and  Arithmetic 
of  the  Greeks  and  Indians,  even  in  their  first  and  most 
scanty  form,  contained  none  but  true  propositions.  Men's 
intuitions  upon  these  subjects  never  allowed  them  to 
slide  into  error  and  confusion  ;  and  the  truths  to  which 
they  were  led  by  the  first  efforts  of  their  faculties,  so 
employed,  form  part  of  the  present  stock  of  our  mathe- 
matical knowledge. 

2.  But  we  are  here  not  so  much  concerned  with  mathe- 
matics in  their  pure  form,  as  with  their  application  to  the 
phenomena  and  laws  of  nature.  And  here  also  the  very 
earliest  history  of  civilization  presents  to  us  some  of  the 
most  remarkable  examples  of  man's  success  in  his  attempts 
to  attain  to  science.  Space  and  time,  position  and  motion, 
govern  all  visible  objects ;  but  by  far  the  most  conspicuous 
examples  of  the  relations  which  arise  out  of  such  elements, 
are  displayed  by  the  ever-moving  luminaries  of  the  sky, 
which  measure  days,  and  months,  and  years,  by  their 
motions,  and  man's  place  on  the  earth  by  their  position. 


INDUCTIVE   APPLICATION    OF    MATHEMATICS.          149 

Hence  the  sciences  of  space  and  number  were  from  the 
first  cultivated  with  peculiar  reference  to  Astronomy.  I 
have  elsewhere*  quoted  Plato's  remark, — that  it  is  absurd 
to  call  the  science  of  the  relations  of  space  geometry,  the 
measure  of  the  earth,  since  its  most  important  office  is  to 
be  found  in  its  application  to  the  heavens.  And  on  other 
occasions  also  it  appears  how  strongly  he,  who  may  be 
considered  as  the  representative  of  the  scientific  and 
speculative  tendencies  of  his  time  and  country,  had  been 
impressed  with  the  conviction,  that  the  formation  of  a 
science  of  the  celestial  motions  must  depend  entirely 
upon  the  progress  of  mathematics.  In  the  Epilogue  to 
the  Dialogue  on  the  Laws^,  he  declares  mathematical 
knowledge  to  be  the  first  and  main  requisite  for  the 
astronomer,  and  describes  the  portions  of  it  which  he 
holds  necessary  for  astronomical  speculators  to  culti- 
vate. These  seem  to  be,  Plane  Geometry,  Theoretical 
Arithmetic,  the  Application  of  Arithmetic  to  planes 
and  to  solids,  and  finally  the  doctrine  of  Harmonics. 
Indeed  the  bias  of  Plato  appears  to  be  rather  to  con- 
sider mathematics  as  the  essence  of  the  science  of 
astronomy,  than  as  its  instrument;  and  he  seems  dis- 
posed, in  this  as  in  other  things,  to  disparage  observation, 
and  to  aspire  after  a  science  founded  upon  demon- 
stration alone.  "An  astronomer,"  he  says  in  the  same 
place,  "must  not  be  like  Hesiod  and  persons  of  that 
kind,  whose  astronomy  consists  in  noting  the  settings 
and  risings  of  the  stars ;  but  he  must  be  one  who 
understands  the  revolutions  of  the  celestial  spheres,  each 
performing  its  proper  cycle." 

A  large  portion  of  the  mathematics  of  the  Greeks, 
so  long  as  their  scientific  activity  continued,  was  directed 
towards  astronomy.  Besides  many  curious  propositions 
of  plane  and  solid  Geometry,  to  which  their  astronomers 

*  Hist.  Ind.  Sc.,  i.  161.  t  Epinomis,  p.  990. 


150  PHILOSOPHY   OF   THE   PURE   SCIENCES. 

were  led,  their  Arithmetic,  though  very  inconvenient  in 
its  fundamental  assumptions,  was  cultivated  to  a  great 
extent ;  and  the  science  of  Trigonometry,  in  which  pro- 
blems concerning  the  relations  of  space  were  resolved  by 
means  of  tables  of  numerical  results  previously  obtained, 
was  created.  Menelaus  of  Alexandria  wrote  six  Books 
on  Chords,  probably  containing  methods  of  calculating 
Tables  of  these  quantities  ;  such  Tables  were  familiarly 
used  by  the  later  Greek  astronomers.  The  same  author 
also  wrote  three  Books  on  Spherical  Trigonometry,  which 
are  still  extant. 

3.  The  Greeks,  however,  in  the  first  vigour  of  their  pur- 
suit of  mathematical  truth,  at  the  time  of  Plato  and  soon 
after,  had  by  no  means  confined  themselves  to  those 
propositions  which  had   a   visible   bearing  on  the  phe- 
nomena of  nature ;   but  had  followed  out  many  beau- 
tiful   trains   of   research,    concerning    various    kinds  of 
figures,  for  the  sake  of  their  beauty  alone  ;  as  for  instance 
in  their  doctrine  of  Conic  Sections,  of  which  curves  they 
had  discovered  all  the  principal  properties.     But  it  is 
curious  to  remark,  that  these  investigations,  thus  pursued 
at   first  as  mere  matters    of  curiosity  and   intellectual 
gratification,  were  destined,  two  thousand  years  later,  to 
play  a  very  important  part  in  establishing  that  system 
of  the  celestial  motions  which  succeeded  the  Platonic 
scheme  of  cycles  and  epicycles.     If  the  properties  of  the 
conic  sections  had  not  been  demonstrated  by  the  Greeks, 
and  thus  rendered  familiar  to  the  mathematicians  of  suc- 
ceeding ages,  Kepler  would  probably  not  have  been  able 
to  discover  those  laws  respecting  the  orbits  and  motions 
of  the  planets  which  were  the  occasion  of  the  greatest 
revolution  that  ever  happened  in  the  history  of  science. 

4.  The  Arabians,  who,  as  I  have  elsewhere  said,  added 
little  of  their  own  to  the  stores  of  science  which  they 
received  from  the  Greeks,  did  however  make  some  very 


INDUCTIVE   APPLICATION   OF   MATHEMATICS.         151 

important  contributions  in  those  portions  of  pure  mathe- 
matics which  are  subservient  to  astronomy.  Their  adop- 
tion of  the  Indian  mode  of  computation  by  means  of  the 
Ten  Digits,  1,  2,  3,  4,  5,  6,  7,  8,  9,  0,  and  by  the  method 
of  Local  Values,  instead  of  the  cumbrous  sexagesimal 
arithmetic  of  the  Greeks,  was  an  improvement  by  which 
the  convenience  and  facility  of  numerical  calculations  were 
immeasurably  augmented.  The  Arabians  also  rendered 
several  of  the  processes  of  trigonometry  much  more 
commodious,  by  using  the  Sine  of  an  arc  instead  of  the 
Chord;  an  improvement  which  Albategnius  appears  to 
claim  for  himself*;  and  by  employing  also  the  Tangents 
of  arcs,  or,  as  they  called  themf,  upright  shadows. 

5.  The  constant  application  of  mathematical  knowledge 
to  the  researches  of  Astronomy,  and  the  mutual  influence 
of  each  science  on  the  progress  of  the  other,  has  been 
still  more  conspicuous  in  modem  times.  Newton's 
Method  of  Prime  and  Ultimate  Ratios,  which  we  have 
already  noticed  as  the  first  correct  exposition  of  the 
doctrine  of  a  Limit,  is  stated  in  a  series  of  Lemmas,  or 
preparatory  theorems,  prefixed  to  his  Treatise  on  the  System 
of  the  World.  Both  the  properties  of  curve  lines  and  the 
doctrines  concerning  force  and  motion,  which  he  had  to 
establish,  required  that  the  common  mathematical  methods 
should  be  methodized  and  extended.  If  Newton  had 
not  been  a  most  expert  and  inventive  mathematician,  as 
well  as  a  profound  and  philosophical  thinker,  he  could 
never  have  made  any  one  of  those  vast  strides  in  disco- 
very of  which  the  rapid  succession  in  his  work  strikes  us 
with  wonder  t-  And  if  we  see  that  the  great  task  begun 
by  him,  goes  on  more  slowly  in  the  hands  of  his  imme- 
diate successors,  and  lingers  a  little  before  its  full  comple- 
tion, we  perceive  that  this  arises,  in  a  great  measure,  from 

*  DELAMBRE,  Ast.,  M.  A.,  p.  12.  t  Ibid.,  p.  17. 

t  Hist.  Ind.  Se.,  ii.,  155.  167.  176. 


152  PHILOSOPHY   OF    THE    PURE    SCIENCES. 

the  defect  of  the  mathematical  methods  then  used.  New- 
ton's synthetical  modes  of  investigation,  as  we  have  else- 
where observed,  were  an  instrument*,  powerful  indeed 
in  his  mighty  hand,  but  too  ponderous  for  other  persons 
to  employ  with  effect.  The  countrymen  of  Newton 
clung  to  it  the  longest,  out  of  veneration  for  their 
master ;  and  English  cultivators  of  physical  astronomy 
were,  on  that  very  account,  left  behind  the  progress  of 
mathematical  science  in  France  and  Germany,  by  a  wide 
interval,  which  they  have  only  recently  recovered.  On 
the  Continent,  the  advantages  offered  by  a  familiar  use  of 
symbols,  and  by  attention  to  their  symmetry  and  other 
relations,  were  accepted  without  reserve.  In  this  manner 
the  Differential  Calculus  of  Leibnitz,  which  was  in  its 
origin  and  signification  identical  with  the  Method  of 
Fluxions  of  Newton,  soon  surpassed  its  rival  in  the 
extent  and  generality  of  its  application  to  problems. 
This  Calculus  was  applied  to  the  science  of  mechanics,  to 
which  it,  along  with  the  symmetrical  use  of  co-ordinates, 
gave  a  new  form  ;  for  it  was  soon  seen  that  the  most 
difficult  problems  might  in  general  be  reduced  to  finding 
integrals,  which  is  the  reciprocal  process  of  that  by  which 
differentials  are  found  ;  so  that  all  difficulties  of  physical 
astronomy  were  reduced  to  difficulties  of  symbolical  cal- 
culation, these,  indeed,  being  often  sufficiently  stubborn. 
Clairaut,  Euler,  and  D'Alembert  employed  the  increased 
resources  of  mathematical  science  upon  the  Theory  of 
the  Moon,  and  other  questions  relative  to  the  system  of 
the  world ;  and  thus  began  to  pursue  such  inquiries  in 
the  course  in  which  mathematicians  are  still  labouring  up 
to  the  present  day.  This  course  was  not  without  its  checks 
and  perplexities.  We  have  elsewhere  quoted  f  Clairaut's 
expression  when  he  had  obtained  the  very  complex 
differential  equations  which  contain  the  solution  of  the 

*  Hist.  Ind.  Sc.>  ii.,  167.  t  /$.,  ii.,  103. 


INDUCTIVE   APPLICATION   OF   MATHEMATICS.         153 

problem  of  the  moon's  motion :  "  Now  integrate  them 
who  can  !"  But  in  no  very  long  time  they  were  inte- 
grated, at  least  approximately ;  and  the  methods  of 
approximation  have  since  then  been  improved ;  so  that 
now,  with  a  due  expenditure  of  labour,  they  may  be 
carried  to  any  extent  which  is  thought  desirable.  If  the 
methods  of  astronomical  observation  should  hereafter 
reach  a  higher  degree  of  exactness  than  they  now  profess, 
so  that  irregularities  in  the  motions  of  the  sun,  moon,  and 
planets,  shall  be  detected  which  at  present  escape  us,  the 
mathematical  part  of  the  theory  of  universal  gravitation  is 
in  such  a  condition  that  it  can  soon  be  brought  into  com- 
parison with  the  newly-observed  facts.  Indeed  at  present 
the  mathematical  theory  is  in  advance  of  such  observa- 
tions. It  can  venture  to  suggest  what  may  afterwards 
be  detected,  as  well  as  to  explain  what  has  already  been 
observed.  This  has  happened  recently;  for  Professor 
Airy  has  calculated  the  law  and  amount  of  an  inequality 
depending  upon  the  mutual  attraction  of  the  Earth  and 
Venus ;  of  which  inequality  (so  small  is  it,)  it  remains  to 
be  determined  whether  its  effect  can  be  traced  in  the 
series  of  astronomical  observations. 

6.  As  the  influence  of  mathematics  upon  the  progress 
of  astronomy  is  thus  seen  in  the  cases  in  which  theory  and 
observation  confirm  each  other,  so  this  influence  appears 
in  another  way,  in  the  very  few  cases  in  which  the  facts 
have  not  been  fully  reduced  to  an  agreement  with  theory. 
The  most  conspicuous  case  of  this  kind  is  the  state  of  our 
knowledge  of  the  Tides.  This  is  a  portion  of  astronomy : 
for  the  Newtonian  theory  asserts  these  curious  phenomena 
to  be  the  result  of  the  attraction  of  the  sun  and  moon. 
Nor  can  there  be  any  doubt  that  this  is  true,  as  a  general 
statement;  yet  the  subject  is  up  to  the  present  time  a 
blot  on  the  perfection  of  the  theory  of  universal  gravita- 
tion ;  for  we  are  very  far  from  being  able  in  this,  as  in  the 


154  PHILOSOPHY   OF  THE   PURE   SCIENCES. 

other  parts  of  astronomy,  to  show  that  theory  will  exactly 
account  for  the  time,  and  magnitude,  and  all  other  cir- 
cumstances of  the  phenomenon  at  every  place  on  the 
earth's  surface.  And  what  is  the  portion  of  our  mathe- 
matics which  is  connected  with  this  solitary  signal  defect 
in  astronomy  ?  It  is  the  mathematics  of  the  Motion  of 
Fluids ;  a  portion  in  which  extremely  little  progress  has 
been  made,  and  in  which  all  the  more  general  problems 
of  the  subject  have  hitherto  remained  entirely  insoluble. 
The  attempts  of  the  greatest  mathematicians,  Newton, 
Maclaurin,  Bernoulli,  Clairaut,  Laplace,  to  master  such 
questions,  all  involve  some  gratuitous  assumption,  which 
is  introduced  because  the  problem  cannot  otherwise  be 
mathematically  dealt  with :  these  assumptions  confessedly 
render  the  result  defective,  and  how  defective  it  is  hard  to 
say.  And  it  was  probably  precisely  the  absence  of  a  theory 
which  could  be  reasonably  expected  to  agree  with  the 
observations,  which  made  Observations  of  this  very  curious 
phenomenon,  the  Tides,  to  be  so  much  neglected  as  till 
very  recently  they  were.  Of  late  years  such  observations 
have  been  pursued,  and  their  results  have  been  resolved 
into  empirical  laws,  so  that  the  rules  of  the  phenomena 
have  been  ascertained,  although  the  dependence  of  these 
rules  upon  the  lunar  and  solar  forces  has  not  been  shown. 
Here  then  we  have  a  portion  of  our  knowledge  relating  to 
facts  undoubtedly  dependent  upon  universal  gravitation, 
in  which  Observation  has  outstripped  Theory  in  her  pro- 
gress, and  is  compelled  to  wait  till  her  usual  companion 
overtakes  her.  This  is  a  position  of  which  Theory  has 
usually  been  very  impatient,  and  we  may  expect  that  she 
will  be  no  less  so  in  the  present  instance. 

7.  It  would  be  easy  to  show  from  the  history  of  other 
sciences,  for  example,  Mechanics  and  Optics,  how  essential 
the  cultivation  of  pure  mathematics  has  been  to  their 
progress.  The  parabola  was  already  familiar  among 


INDUCTIVE   APPLICATION   OF   MATHEMATICS.          155 

mathematicians  when  Galileo  discovered  that  it  was  the 
theoretical  path  of  a  Projectile ;  and  the  extension  and 
generalization  of  the  Laws  of  Motion  could  never  have 
been  effected,  unless  the  differential  and  integral  calculus 
had  been  at  hand,  ready  to  trace  the  results  of  every  hypo- 
thesis which  could  be  made.  D'Alembert's  mode  of 
expressing  the  Third  Law  of  Motion  in  its  most  general 
form*,  if  it  did  not  prove  the  law,  at  least  reduced  the 
application  of  it  to  analytical  processes  which  could  be  per- 
formed in  most  of  those  cases  in  which  they  were  needed. 
In  many  instances  the  demands  of  mechanical  science 
suggested  the  extension  of  the  methods  of  pure  analysis. 
The  problem  of  Vibrating  Strings  gave  rise  to  the  Calculus 
of  Partial  Differences,  which  was  still  further  stimulated 
by  its  application  to  the  motions  of  fluids  and  other 
mechanical  problems.  And  we  have  in  the  writings  of 
Lagrange  and  Laplace  other  instances  equally  remarkable 
of  new  analytical  methods,  to  which  mechanical  problems, 
and  especially  cosmical  problems.,  have  given  occasion. 

8.  The  progress  of  Optics  as  a  science  has,  in  like  manner, 
been  throughout  dependent  upon  the  progress  of  pure 
mathematics.  The  first  rise  of  geometry  was  followed  by 
some  advances,  slight  ones  no  doubt,  in  the  doctrine  of 
Reflection  and  in  Perspective.  The  law  of  Refraction  was 
traced  to  its  consequences  by  means  of  trigonometry, 
which  indeed  was  requisite  to  express  the  law  in  a  simple 
form.  The  steps  made  in  optical  science  by  Descartes, 
Newton,  Euler,  and  Huyghens,  required  the  geometrical 
skill  which  those  philosophers  possessed.  And  if  Young 
and  Fresnel  had  not  been,  each  in  his  peculiar  way,  per- 
sons of  eminent  mathematical  endowments,  they  would 
not  have  been  able  to  bring  the  Theory  of  Undulations 
and  Interferences  into  a  condition  in  which  it  could  be 
tested  by  experiments.  We  may  see  how  unexpectedly 

*  Hist.  Ind.  &•„  ii.  89. 


156  PHILOSOPHY   OF  THE   PURE   SCIENCES. 

recondite  parts  of  pure  mathematics  may  bear  upon  phy- 
sical science,  by  calling  to  mind  a  circumstance  already 
noticed  in  the  History  of  Science*; — that  Fresnel 
obtained  one  of  the  most  curious  confirmations  of  the 
theory  (the  laws  of  Circular  Polarization  by  reflection) 
through  an  interpretation  of  an  algebraical  expression, 
which,  according  to  the  original  conventional  meaning  of 
the  symbols,  involved  an  impossible  quantity.  We  have 
already  remarked,  that  in  virtue  of  the  principle  of  the 
generality  of  symbolical  language,  such  an  interpretation 
may  often  point  out  some  real  and  important  analogy. 

8.  From  this  rapid  sketch  it  may  be  seen  how  important 
an  office  in  promoting  the  progress  of  the  physical  sciences 
belongs  to  mathematics.  Indeed  in  the  progress  of  many 
sciences  every  step  has  been  so  intimately  connected  with 
some  advance  in  mathematics,  that  we  can  hardly  be 
surprised  if  some  persons  have  considered  mathematical 
reasoning  to  be  the  most  essential  part  of  such  sciences ; 
and  have  overlooked  the  other  elements  which  enter  into 
their  formation.  How  erroneous  this  view  is  we  shall 
best  see  by  turning  our  attention  to  the  other  Ideas  besides 
those  of  space,  number,  and  motion,  which  enter  into 
some  of  the  most  conspicuous  and  admired  portions  of 
what  is  termed  exact  science ;  and  by  showing  that  the 
clear  and  distinct  developement  of  such  Ideas  is  quite 
as  necessary  to  the  progress  of  exact  and  real  knowledge 
as  an  acquaintance  with  arithmetic  and  geometry. 

*  Vol.  ii.  445. 


157 


BOOK   III. 


THE  PHILOSOPHY  OF  THE  MECHANICAL 
SCIENCES. 


CHAPTER  I. 
OF  THE  MECHANICAL  SCIENCES. 

IN  the  History  of  the  Sciences,  that  class  of  which  we 
here  speak  occupies  a  conspicuous  and  important  place ; 
coming   into   notice    immediately   after   those   parts   of 
astronomy  which  require  for  their  cultivation  merely  the 
ideas  of  space,  time,  motion,  and  number.     It  appears 
from  our  History  that  certain  truths  concerning  the  equi- 
librium of  bodies  were  established  by  Archimedes ;  that, 
after  a  long  interval  of  inactivity,  his  principles  were 
extended  and  pursued  further   in   modern    times:    and 
that  to  these  doctrines  concerning  equilibrium  and  the 
forces  which  produce  it,  (which  constitute  the  science 
Statics,}  were  added  many  other  doctrines  concerning  the 
motions  of  bodies,  considered  also  as  produced  by  forces, 
and  thus  the  science  of  Dynamics  was  produced.     The 
assemblage  of  these  sciences  composes  the  province  of 
Mechanics.      Moreover,   philosophers   have   laboured   to 
make  out  the  laws  of  the  equilibrium  of  fluid  as  well  as 
solid  bodies ;  and  hence  has  arisen  the  science  of  Hydro- 
statics.   And  the  doctrines  of  Mechanics  have  been  found 
to  have  a  most  remarkable  bearing  upon  the  motions  of 
the  heavenly  bodies;  with  reference  to  which,  indeed, 
they  were  at  first  principally  studied.     The  explanation  of 


158         PHILOSOPHY   OF   THE   MECHANICAL   SCIENCES. 

those  cosmical  facts  by  means  of  mechanical  principles 
and  their  consequences,  forms  the  science  of  Physical 
Astronomy.  These  are  the  principal  examples  of  mecha- 
nical science ;  although  some  other  portions  of  Physics, 
as  Magnetism  and  Electrodynamics,  introduce  mecha- 
nical doctrines  very  largely  into  their  speculations. 

Now  in  all  these  sciences  we  have  to  consider  Forces. 
In  all  mechanical  reasonings  forces  enter,  either  as 
producing  motion,  or  as  prevented  from  doing  so  by  other 
forces.  Thus  force,  in  its  most  general  sense,  is  the  came 
of  motion,  or  of  tendency  to  motion ;  and  in  order  to 
discover  the  principles  on  which  the  mechanical  sciences 
truly  rest,  we  must  examine  the  nature  and  origin  of  our 
knowledge  of  Causes. 

In  these  sciences,  however,  we  have  not  to  deal  with 
Cause  in  its  more  general  acceptation,  in  which  it  applies 
to  all  kinds  of  agency,  material  or  immaterial ; — to  the 
influence  of  thought  and  will,  as  well  as  of  bodily  pressure 
and  attractive  force.  Our  business  at  present  is  only 
with  such  causes  as  immediately  operate  upon  matter. 
We  shall  nevertheless,  in  the  first  place,  consider  the 
nature  of  Cause  in  its  most  general  form ;  and  afterwards 
narrow  our  speculations  so  as  to  direct  them  specially 
to  the  mechanical  sciences. 


CHAPTER  II. 
OF  THE   IDEA  OF  CAUSE. 

1.  WE  see  in  the  world  around  us  a  constant  succes- 
sion of  causes  and  effects  connected  with  each  other. 
The  laws  of  this  connexion  we  learn  in  a  great  measure 
from  experience,  by  observation  of  the  occurrences  which 
present  themselves  to  our  notice,  succeeding  one  another. 


OF   THE   IDEA   OF   CAUSE.  159 

But  in  doing  this,  and  in  attending  to  this  succession  of 
appearances,  of  which  we  are  aware  by  means  of  our  senses, 
we  supply  from  our  own  minds  the  Idea  of  Cause.  This 
Idea,  as  we  have  already  shown  with  respect  to  other 
Ideas,  is  not  derived  from  experience,  but  has  its  origin 
in  the  mind  itself; — is  introduced  into  our  experience  by 
the  active,  and  not  by  the  passive  part  of  our  nature. 

By  Cause  we  mean  some  quality,  power,  or  efficacy, 
by  which  a  state  of  things  produces  a  succeeding  state. 
Thus  the  motion  of  bodies  from  rest  is  produced  by  a 
cause  which  we  call  Force :  and  in  the  particular  case  in 
which  bodies  fall  to  the  earth,  this  force  is  termed  Gra- 
vity. In  these  cases,  the  Conceptions  of  Force  and  Gra- 
vity receive  their  meaning  from  the  Idea  of  Cause 
which  they  involve :  for  Force  is  conceived  as  the  Cause 
of  Motion.  That  this  Idea  of  Cause  is  not  derived  from 
experience,  we  prove  (as  in  former  cases)  by  this  con- 
sideration: that  we  can  make  assertions,  involving  this 
idea,  which  are  rigorously  necessary  and  universal; 
whereas  knowledge  derived  from  experience  can  only  be 
true  as  far  as  experience  goes,  and  can  never  contain  in 
itself  any  evidence  whatever  of  its  necessity.  We  assert 
that  "  Every  event  must  have  a  cause :"  and  this  proposi- 
tion we  know  to  be  true,  not  only  probably,  and  gene- 
rally, and  as  far  as  we  can  see :  but  we  cannot  suppose 
it  to  be  false  in  any  single  instance.  We  are  as  certain 
of  it  as  of  the  truths  of  arithmetic  or  geometry.  We 
cannot  doubt  that  it  must  apply  to  all  events  past  and 
future,  in  every  part  of  the  universe,  just  as  truly  as  to 
those  occurrences  which  we  have  ourselves  observed. 
What  causes  produce  what  effects ; — what  is  the  cause  of 
any  particular  event ;  what  will  be  the  effect  of  any  pecu- 
liar process ;  these  are  points  on  which  experience  may 
enlighten  us.  Observation  and  experience  may  be  requi- 
site, to  enable  us  to  judge  respecting  such  matters.  But 


160         PHILOSOPHY    OF    THE   MECHANICAL    SCIENCES. 

that  every  event  has  some  cause,  Experience  cannot  prove 
any  more  than  she  can  disprove.  She  can  add  nothing 
to  the  evidence  of  the  truth,  however  often  she  may 
exemplify  it.  This  doctrine,  then,  cannot  have  been 
acquired  by  her  teaching :  and  the  Idea  of  Cause,  which 
the  doctrine  involves,  and  on  which  it  depends,  cannot 
have  come  into  our  minds  from  the  region  of  observa- 
tion. 

2.  That  we  do,  in  fact,  apply  the  Idea  of  Cause  in  a 
more  extensive  manner  than  could  be  justified,  if  it  were 
derived  from  experience  only,  is  easily  shown.     For  from 
the  principle  that  everything^must  have  a  cause,  we  not 
only  reason  concerning  the  succession  of  events  which 
occur  in  the  progress  of  the  world,  and  which  form  the 
course  of  experience ;  but  we  infer  that  the  world  itself 
must  have  a  cause ;  that  the  chain  of  events  connected 
by  common   causation,  must   have  a  First  Cause  of  a 
nature  different  from  the  events  themselves.     This  we 
are  entitled  to  do,  if  our  Idea  of  Cause  be  independent  of, 
and  superior  to,  experience :  but  if  we  have  no  Idea  of 
Cause  except  such   as  we  gather  from  experience,  this 
reasoning  is  altogether  baseless  and  unmeaning. 

3.  Again ;  by  the  use  of  our  powers  of  observation, 
we  are  aware  of  a  succession  of  appearances  and  events. 
But  none  of  our  senses  or  powers  of  external  observation 
can  detect  in  these   appearances  the  power  or  quality 
which  we  call  Cause.     Cause  is  that  which  connects  one 
event  with  another ;  but  no  sense  or  perception  discloses 
to  us,  or  can  disclose,  any  connexion  among  the  events 
which  we  observe.     We  see  that  one  occurrence  follows 
another,  but  we  can  never  see  anything  which  shows  that 
one  occurrence  must  follow  another.     We  have  already 
noticed*,  that  this  truth  has  been  urged  by  metaphysi- 
cians in  modern  times,  and  generally  assented  to  by  those 

*  Book  i.,  chap.  13. 


OF    THE    IDEA    OF    CAUSE.  161 

who  examine  carefully  the  connexion  of  their  own 
thoughts.  The  arguments  are,  indeed,  obvious  enough. 
One  ball  strikes  another  and  causes  it  to  move  forwards. 
But  by  what  compulsion?  Where  is  the  necessity? 
If  the  mind  can  see  any  circumstance  in  this  case  which 
makes  the  result  inevitable,  let  this  circumstance  be 
pointed  out.  But,  in  fact,  there  is  no  such  discoverable 
necessity;  for  we  can  conceive  this  event  not  to  take 
place  at  all.  The  struck  ball  may  stand  still,  for  aught 
we  can  see.  "  But  the  laws  of  motion  will  not  allow  it  to 
do  so."  Doubtless  they  will  not.  But  the  laws  of  motion 
are  learnt  from  experience,  and  therefore  can  prove  no 
necessity.  Why  should  not  the  laws  of  motion  be  other 
than  they  are  ?  Are  they  necessarily  true  ?  That  they 
are  necessarily  such  as  do  actually  regulate  the  impact  of 
bodies,  is  at  least  no  obvious  truth ;  and  therefore  this 
necessity  cannot  be,  in  common  minds,  the  ground  of 
connecting  the  impact  of  one  ball  with  the  motion  of 
another.  And  assuredly,  if  this  fail,  no  other  ground  of 
such  necessary  connexion  can  be  shown.  In  this  case, 
then,  the  events  are  not  seen  to  be  necessarily  connected. 
But  if  this  case,  where  one  ball  moves  another  by  impulse, 
be  not  an  instance  of  events  exhibiting  a  necessary  con- 
nexion, we  shall  look  in  vain  for  any  example  of  such  a 
connexion.  There  is,  then,  no  case  in  which  events  can 
be  observed  to  be  necessarily  connected :  our  idea  of 
causation,  which  implies  that  the  event  is  necessarily 
connected  with  the  cause,  cannot  be  derived  from  obser- 
vation. 

4.  But  it  may  be  said,  we  have  not  any  such  idea  of 
cause,  implying  necessary  connexion  with  effect,  and  a 
quality  by  which  this  connexion  is  produced.  We  see 
nothing  but  the  succession  of  events ;  and  by  cause  we 
mean  nothing  but  a  certain  succession  of  events ;— namely, 
a  constant,  unvarying  succession.  Cause  and  effect  are 
VOL.  i.  M 


162         PHILOSOPHY    OF   THE   MECHANICAL   SCIENCES. 

only  two  events  of  which  the  second  invariably  follows 
the  first.  We  delude  ourselves  when  we  imagine  that 
our  idea  of  causation  involves  anything  more  than  this. 

To  this  I  reply  by  asking,  what  then  is  the  meaning 
of  the  maxim  above  quoted,  and  allowed  by  all  to  be 
universally  and  necessarily  true,  that  every  event  must 
have  a  cause  ?  Let  us  put  this  maxim  into  the  language 
of  the  explanation  just  noticed ;  and  it  becomes  this : — 
"  Every  event  must  have  a  certain  other  event  invariably 
preceding  it."  But  why  must  it  ?  Where  is  the  necessity? 
Why  must  like  events  always  be  preceded  by  like,  except 
so  far  as  other  events  interfere  ?  That  there  is  such  a 
necessity,  no  one  can  doubt.  All  will  allow  that  if  a  stone 
ascend  because  it  is  thrown  upwards  in  one  case,  a  stone 
which  ascends  in  another  case  has  also  been  thrown  up- 
wards, or  has  undergone  some  equivalent  operation.  All 
will  allow  that  in  this  sense,  every  kind  of  event  must 
have  some  other  specific  kind  of  event  preceding  it.  But 
this  turn  of  men's  thoughts  shows  that  they  see  in  events 
a  connexion  which  is  not  mere  succession.  They  see  in 
cause  and  effect,  not  merely  what  does,  often  or  always, 
precede  and  follow,  but  what  must  precede  and  follow. 
The  events  are  not  only  conjoined,  they  are  connected. 
The  cause  is  more  than  the  prelude,  the  effect  is  more 
than  the  sequel,  of  the  fact.  The  cause  is  conceived  not 
as  a  mere  occasion ;  it  is  a  power,  an  efficacy,  which  has 
a  real  operation. 

5.  Thus  we  have  drawn  from  the  maxim,  that  every 
effect  must  have  a  cause,  arguments  to  show  that  we 
have  an  idea  of  cause  which  is  not  borrowed  from  expe- 
rience, and  which  involves  more  than  mere  succession. 
Similar  arguments  might  be  derived  from  any  other 
maxims  of  universal  and  necessary  validity,  which  we 
can  obtain  concerning  cause  :  as,  for  example,  the  maxims 
that  causes  are  measured  by  their  effects,  and  that  reac- 


OF    THE    IDEA    OF    CAUSE.  163 

tion  is  equal  and  opposite  to  action.  These  maxims  we 
shall  soon  have  to  examine ;  but  we  may  observe  here, 
that  the  necessary  truth  which  belongs  to  them,  shows 
that  they,  and  the  ideas  they  involve,  are  not  the  mere 
fruits  of  observation  ;  while  their  meaning,  containing,  as 
it  does,  something  quite  different  from  the  mere  concep- 
tion of  succession  of  events,  proves  that  such  a  conception 
is  far  from  containing  the  whole  import  and  signification 
of  our  idea  of  cause. 

The  progress  of  the  opinions  of  philosophers  on  the 
points  discussed  in  this  chapter,  has  been  one  of  the  most 
remarkable  parts  of  the  history  of  Metaphysics  in  modern 
times:  and  I  shall  therefore  briefly  notice  some  of  its 
features. 


CHAPTER  III. 

MODERN  OPINIONS  RESPECTING  THE  IDEA 
OF  CAUSE. 

1.  TOWARDS  the  end  of  the  seventeenth  century  there 
existed  in  the  minds  of  many  of  the  most  vigorous  and 
active  speculators  of  the  European  literary  world,  a  strong 
tendency  to  ascribe  the  whole  of  our  knowledge  to  the 
teaching  of  experience.  This  tendency,  with  its  conse- 
quences, including  among  them  the  reaction  which  was 
produced  when  the  tenet  had  been  pushed  to  a  length 
manifestly  absurd,  has  exercised  a  very  powerful  influence 
upon  the  progress  of  metaphysical  doctrines  up  to  the 
present  time.  I  proceed  to  notice  some  of  the  most 
prominent  of  the  opinions  which  have  thus  obtained 
prevalence  among  philosophers,  so  far  as  the  Idea  of 
Cause  is  concerned. 

Locke  was  one  of  the  metaphysicians  who  produced 
the  greatest  effect  in  diffusing  this  opinion,  of  the  exclusive 

M  2 


164          PHILOSOPHY  OF  THE  MECHANICAL  SCIENCES. 

dependence  of  our  knowledge  upon  experience.  Agree- 
ably to  this  general  system,  he  taught*  that  our  ideas  of 
Cause  and  Effect  are  got  from  observation  of  the  things 
about  us.  Yet  notwithstanding  this  tenet  of  his,  he 
endeavoured  still  to  employ  these  ideas  in  reasoning  on 
subjects  which  are  far  beyond  all  limits  of  experience : 
for  he  professed  to  prove,  from  our  idea  of  Causation, 
the  existence  of  the  Deityf . 

Hume  noticed  this  obvious  inconsistency;  but  declared 
himself  unable  to  discover  any  remedy  for  a  defect  so 
fatal  to  the  most  important  parts  of  our  knowledge.     He 
could  see,  in  our  belief  of  the  succession  of  cause  and 
effect,  nothing  but  the  habit  of  associating  in  our  minds 
what  had  often  been  associated  in  our  experience.     He 
therefore   maintained    that  we  could   not,  with   logical 
propriety,  extend  our  belief  of  such  a  succession  to  cases 
entirely  distinct  from  all  those  of  which  our  experience 
consisted.     We  see,  he  said,  an  actual  conjunction  of  two 
events ;  but  we  can  in  no  way  detect  a  necessary  con- 
nexion ;  and  therefore  we  have  no  means  of  inferring 
cause  from  effect,  or  effect  from  cause  $.     The  only  way 
in  which  we  recognise  cause  and  effect  in  the  field  of  our 
experience,  is  as  an  unfailing  sequence  :  we  look  in  vain 
for  anything  which  can  assure  us  of  an  infallible  conse- 
quence.    And  since  experience  is  the  only  source  of  our 
knowledge,  we  cannot  with  any  justice  assert  that  the 
world  in  which  we  live  must  necessarily  have  had  a  cause. 
2.  This  doctrine,  taken  in  conjunction  with  the  known 
scepticism  of  its  author  on  religious  points,  produced  a 
considerable  fermentation  in  the  speculative  world.     The 
solution  of  the  difficulty  thus  thrown  before  philosophers, 
was  by  no  means  obvious.     It  was  vain  to  endeavour  to 
find  in  experience  any  other  property  of  a  cause  than  a 

*  Essay  on  the  Human  Understanding,  b.  ii.,  c.  26.         t  B.  iv.,  c.  10. 
J  HUME'S  Phil,  of  the  Human  Mind,  vol.  i.,  p.  94. 


OPINIONS   RESPECTING   THE    IDEA    OF    CAUSE.          165 

constant  sequence  of  the  effect.  Yet  it  was  equally  vain 
to  try  to  persuade  men  that  they  had  no  idea  of  cause ; 
or  even  to  shake  their  belief  in  the  cogency  of  the  fami- 
liar arguments  concerning  the  necessity  of  an  original 
cause  of  all  that  is  and  happens.  Accordingly  these 
hostile  and  apparently  irreconcilable  doctrines, — the  in- 
dispensable necessity  of  a  cause  of  every  event,  and  the 
impossibility  of  our  knowing  such  a  necessity, — were  at 
last  allowed  to  encamp  side  by  side.  Reid,  Beattie,  and 
others,  formed  one  party,  who  showed  how  widely  and 
constantly  the  idea  of  a  cause  pervades  all  the  processes 
of  the  human  mind  :  while  another  sect,  including  Brown, 
and  apparently  Stewart,  maintained  that  this  idea  is 
always  capable  of  being  resolved  into  a  constant  sequence ; 
and  these  latter  reasoners  tried  to  obviate  the  dangerous 
and  shocking  inferences  which  some  persons  might  try  to 
draw  from  their  opinion,  by  declaring  the  maxim  that 
"  Every  event  must  have  a  cause,"  to  be  an  instinctive  law 
of  belief,  or  a  fundamental  principle  of  the  human  mind  *. 

3.  While  this  series  of  discussions  was  going  on  in 
Britain,  a  great  metaphysical  genius  in  Germany  was 
unravelling  the  perplexity  in  another  way.  Kant's  spe- 
culations originated,  as  he  informs  us,  in  the  trains  of 
thought  to  which  Hume's  writings  gave  rise;  and  the 
Kritik  der  Reinen  Vernunft,  or  Examination  of  the  Pure 
Reason,  was  published  in  1787,  with  the  view  of  showing 
the  true  nature  of  our  knowledge. 

Kant's  solution  of  the  difficulties  just  mentioned 
differs  materially  from  that  above  stated.  According  to 
Brown  f,  succession  observed  and  cause  inferred,— the 
memory  of  past  conjunctions  of  events  and  the  belief  of 
similar  future  conjunctions. — are  facts,  independent,  so 
far  as  we  can  discover,  but  inseparably  combined  by  a 

*  STEWART'S  Active  Powers,  vol.  i.,  p.  347.     BROWN'S  Lectures^ 
vol.  i.,  p.  115.  t  Lect.^  vol.  i.,  p.  114, 


166       PHILOSOPHY   OF   THE   MECHANICAL   SCIENCES. 

law  of  our  mental  nature.  According  to  Kant,  causality 
is  an  inseparable  condition  of  our  experience :  a  con- 
nexion in  events  is  requisite  to  our  apprehending  them  as 
events.  Future  occurrences  must  be  connected  by  causa- 
tion as  the  past  have  been,  because  we  cannot  think  of 
past,  present,  and  future,  without  such  connexion.  We 
cannot  fix  the  mind  upon  occurrences,  without  including 
these  occurrences  in  a  series  of  causes  and  effects.  The 
relation  of  causation  is  a  condition  under  which  we 
think  of  events,  as  the  relations  of  space  are  a  condition 
under  which  we  see  objects. 

4.  On  a  subject  so  abstruse,  it  is  not  easy  to  make 
our  distinctions  very  clear.  Some  of  Brown's  illustrations 
appear  to  approach  very  near  to  the  doctrine  of  Kant. 
Thus  he  says*,  "  The  form  of  bodies  is  the  relation  of 
their  elements  to  each  other  in  space, — the  power  of 
bodies  is  their  relation  to  each  other  in  time."  Yet  not- 
withstanding such  approximations  in  expression,  the 
Kantian  doctrine  appears  to  be  different  from  the  views 
of  Stewart  and  Brown,  as  commonly  understood.  Ac- 
cording to  the  Scotch  philosophers,  the  cause  and  the 
effect  are  two  things,  connected  in  our  minds  by  a  law 
of  our  nature.  But  this  view  requires  us  to  suppose  that 
we  can  conceive  the  law  to  be  absent,  and  the  course  of 
events  to  be  unconnected.  If  we  can  understand  what 
is  the  special  force  of  this  law,  we  must  be  able  to  imagine 
what  the  case  would  be  if  the  law  were  non-existing.  We 
must  be  able  to  conceive  a  mind  which  does  not  connect 
effects  with  causes.  The  Kantian  doctrine,  on  the  other 
hand,  teaches  that  we  cannot  imagine  events  liberated 
from  the  connexion  of  cause  and  effect :  this  connexion  is 
a  condition  of  our  conceiving  any  real  occurrences  :  we 
cannot  think  of  a  real  sequence  of  things,  except  as  in- 
volving the  operation  of  causes.  In  the  Scotch  system, 
*  Lect.,  i.,  p.  127. 


OPINIONS  RESPECTING  THE   IDEA   OF   CAUSE.        167 

the  past  and  the  future  are  in  their  nature  independent, 
but  bound  together  by  a  rule ;  in  the  German  system, 
they  share  in  a  common  nature  and  mutual  relation,  by 
the  act  of  thought  which  makes  them  past  and  future. 
In  the  former  doctrine  cause  is  a  tie  which  binds ;  in  the 
latter  it  is  a  character  which  pervades  and  shapes  events. 
The  Scotch  metaphysicians  only  assert  the  universality  of 
the  relation ;  the  German  attempts  further  to  explain  its 
necessity. 

This  being  the  state  of  the  case,  such  illustrations  as 
that  of  Dr.  Brown  quoted  above,  in  which  he  represents 
cause  as  a  relation  of  the  same  kind  with  form,  do  not 
appear  exactly  to  fit  his  opinions.  Can  the  relations  of 
figure  be  properly  said  to  be  connected  with  each  other 
by  a  law  of  our  nature,  or  a  tendency  of  our  mental  con- 
stitution ?  Can  we  ascribe  it  to  a  law  of  our  thoughts, 
that  we  believe  the  three  angles  of  a  triangle  to  be  equal 
to  two  right  angles?  If  so,  we  must  give  the  same 
reason  for  our  belief  that  two  straight  lines  cannot 
inclose  a  space ;  or  that  three  and  two  are  five.  But  will 
any  one  refer  us  to  an  ultimate  law  of  our  constitution 
for  the  belief  that  three  and  two  are  five  ?  Do  we  not 
see  that  they  are  so,  as  plainly  as  we  see  that  they  are 
three  and  two  ?  Can  we  imagine  laws  of  our  constitu- 
tion abolished,  so  that  three  and  two  shall  make  some- 
thing different  from  five ; — so  that  an  inclosed  space  shall 
lie  between  two  straight  lines ; — so  that  the  three  angles 
of  a  plane  triangle  shall  be  greater  than  two  right  angles? 
We  cannot  conceive  this.  If  the  numbers  are  three  and 
two ;  if  the  lines  are  straight ;  if  the  triangle  is  a  recti- 
linear triangle,  the  consequences  are  inevitable.  We 
cannot  even  imagine  the  contrary.  We  do  not  want  a 
law  to  direct  that  things  should  be  what  they  are.  The 
relation,  then,  of  cause  and  effect,  being  of  the  same  kind 
as  the  necessary  relations  of  figure  and  number,  is  not 


168        PHILOSOPHY    OF   THE   MECHANICAL   SCIENCES. 

properly  spoken  of  as  established  in  our  minds  by  a  spe- 
cial law  of  our  constitution  :  for  we  reject  that  loose  and 
inappropriate  phraseology  which  speaks  of  the  relations  of 
figure  and  number  as  determined  by  laws  of  belief. 

5.  In  the  present  work,  we  accept  and  adopt,  as  the 
basis  of  our  inquiry  concerning  our  knowledge,  the  exist- 
ence of  necessary  truths  concerning  causes,  as  there  exist 
necessary  truths  concerning  figure  and  number.  We  find 
such  truths  universally  established  and  assented  to  among 
the  cultivators  of  science,  and  among  speculative  men  in 
general.  All  mechanicians  agree  that  reaction  is  equal 
and  opposite  to  action,  both  when  one  body  presses  ano- 
ther, and  when  one  body  communicates  motion  to  another. 
All  reasoners  join  in  the  assertion  not  only  that  every 
observed  change  of  motion  has  had  a  cause,  but  that  every 
change  of  motion  must  have  a  cause.  Here  we  have  cer- 
tain portions  of  substantial  and  undoubted  knowledge. 
Now  the  essential  point  in  the  view  which  we  must  take  of 
the  idea  of  cause  is  this, — that  our  view  must  be  such  as 
to  form  a  solid  basis  for  our  knowledge.  We  have,  in  the 
Mechanical  Sciences,  certain  universal  and  necessary  truths 
on  the  subject  of  causes.  Now  any  view  which  refers 
our  belief  in  causation  to  mere  experience  or  habit,  can- 
not explain  the  possibility  of  such  necessary  truths,  since 
experience  and  habit  can  never  lead  to  a  perception  of 
necessary  connexion.  But  a  view  which  teaches  us  to 
acknowledge  axioms  concerning  cause,  as  we  acknow- 
ledge axioms  concerning  space,  will  lead  us  to  look  upon 
the  science  of  mechanics  as  equally  certain  and  universal 
with  the  science  of  geometry ;  and  will  thus  materially 
affect  our  judgment  concerning  the  nature  and  claims  of 
our  scientific  knowledge. 

Axioms  concerning  cause,  or  concerning  force,  which 
as  we  shall  see,  is  a  modification  of  cause,  will  flow  from 
an  idea  of  cause,  just  as  axioms  concerning  space  and 


.  OPINIONS  RESPECTING  THE  IDEA  OF  CAUSE.  169 

number  flow  from  the  ideas  of  space  and  time.  And 
thus  the  propositions  which  constitute  the  science  of 
mechanics  prove  that  we  possess  an  idea  of  cause,  in  the 
same  sense  in  which  the  propositions  of  geometry  and 
arithmetic  prove  our  possession  of  the  ideas  of  space  and 
of  time  or  number. 

6.  The  idea  of  cause,  like  the  ideas  of  space  and  time, 
is  a  part  of  the  active  powers  of  the  mind.  The  relation  of 
cause  and  effect  is  a  relation  or  condition  under  which 
events  are  apprehended,  which  relation  is  not  given  by  ob- 
servation, but  supplied  by  the  mind  itself.  According  to 
the  views  which  explain  our  apprehension  of  cause  by  refer- 
ence to  habit,  or  to  a  supposed  law  of  our  mental  nature, 
causal  connexion  is  a  consequence  of  agencies  which  the 
mind  passively  obeys ;  but  according  to  the  view  to  which 
we  are  led,  this  connexion  is  a  result  of  faculties  which 
the  mind  actively  exercises.  And  thus  the  relation  of 
cause  and  effect  is  a  condition  of  our  apprehending  suc- 
cessive events,  a  part  of  the  mind's  constant  and  universal 
activity,  a  source  of  necessary  truths ;  or  to  sum  all  this 
in  one  phrase,  a  Fundamental  Idea. 


CHAPTER  IV. 

OF  THE  AXIOMS  WHICH  RELATE  TO  THE  IDEA 

OF  CAUSE. 

1.  Cause  is  an  abstract  Term. — We  have  now  to  ex- 
press, as  well  as  we  can,  the  fundamental  character  of  that 
Idea  of  Cause,  of  which  we  have  just  proved  the  exist- 
ence. This  may  be  done,  at  least  for  purposes  of  reason- 
ing, in  this  as  in  former  instances,  by  means  of  axioms. 
I  shall  state  the  principal  axioms  which  belong  to  this 
subject,  referring  the  reader  to  his  own  thoughts  for  the 
axiomatic  evidence  which  belongs  to  them. 


170       PHILOSOPHY   OP   THE   MECHANICAL   SCIENCES. 

But  I  must  first  observe  that  in  order  to  express 
general  and  abstract  truths  concerning  cause  and  effect, 
these  terms,  cause  and  effect,  must  be  understood  in  a  gene- 
ral and  abstract  manner.  When  one  event  gives  rise  to 
another,  the  first  event  is,  in  common  language,  often 
called  the  cause,  and  the  second  the  effect.  Thus  the 
meeting  of  two  billiard  balls  may  be  said  to  be  the 
cause  of  one  of  them  turning  aside  out  of  the  path  in 
which  it  was  moving.  For  our  present  purposes,  how- 
ever, we  must  not  apply  the  term  cause  to  such  occur- 
rences as  this  meeting  and  turning,  but  to  a  certain  con- 
ception, ybree,  abstracted  from  all  such  special  events,"and 
considered  as  a  quality  or  property  by  which  one  body 
affects  the  motion  of  the  other.  And  in  like  manner  in 
other  cases,  cause  is  to  be  conceived  as  some  abstract 
quality,  power,  or  efficacy,  by  which  change  is  produced ; 
a  quality  not  identical  with  the  events,  but  disclosed  by 
means  of  them.  Not  only  is  this  abstract  mode  of  con- 
ceiving force  and  cause  useful  in  expressing  the  funda- 
mental principles  of  science ;  but  it  supplies  us  with  the 
only  mode  by  which  such  principles  can  be  stated  in  a 
general  manner,  and  made  to  lead  to  substantial  truth  and 
real  knowledge. 

Understanding  cause,  therefore,  in  this  sense,  we 
proceed  to  our  Axioms. 

2.  First  Axiom.  Nothing  can  take  place  without  a 
Cause. 

Every  event,  of  whatever  kind,  must  have  a  Cause  in 
the  sense  of  the  term  which  we  have  just  indicated ;  and 
that  it  must,  is  a  universal  and  necessary  proposition  to 
which  we  irresistibly  assent  as  soon  as  it  is  understood. 
We  believe  each  appearance  to  come  into  existence,  we 
conceive  every  change  to  take  place,  not  only  with  some- 
thing preceding  it,  but  something  by  which  it  is  made  to 
be  what  it  is.  An  effect  without  a  cause ; — an  event  with- 


AXIOMS   WHICH   RELATE   TO   THE   IDEA   OF   CAUSE.      171 

out  a  preceding  condition  involving  the  efficacy  by  which 
the  event  is  produced ; — are  suppositions  which  we  cannot 
for  a  moment  admit.  That  the  connexion  of  effect  with 
cause  is  universal  and  necessary,  is  a  universal  and  con- 
stant conviction  of  mankind.  It  persists  in  the  minds  of 
all  men,  undisturbed  by  all  the  assaults  of  sophistry  and 
scepticism ;  and,  as  we  have  seen  in  the  last  chapter,  re- 
mains unshaken,  even  when  its  foundations  seem  to  be 
ruined.  This  axiom  expresses,  to  a  certain  extent,  our 
Idea  of  cause ;  and  when  that  idea  is  clearly  apprehended, 
the  axiom  requires  no  proof,  and  indeed  admits  of  none 
which  makes  it  more  evident.  That  notwithstanding  its 
simplicity,  it  is  of  use  in  our  speculations,  we  shall  here- 
after see ;  but  in  the  first  place,  we  must  consider  the 
other  axioms  belonging  to  this  subject. 

3.  Second  Axiom.  Effects  are  proportional  to  their 
Causes,  and  Causes  are  measured  by  their  Effects. 

We  have  already  said  that  cause  is  that  quality  or  power 
in  the  circumstances  of  each  case  by  which  the  effect  is 
produced;  and  this  power,  an  abstract  property  of  the 
condition  of  things  to  which  it  belongs,  can  in  no  way 
fall  directly  under  the  cognisance  of  the  senses.  Cause, 
of  whatever  kind,  is  not  apprehended  as  including  objects 
and  events  which  share  its  nature  by  being  co-extensive 
with  certain  portions  of  it,  as  space  and  time  are.  It 
cannot  therefore,  like  them,  be  measured  by  repetition 
of  its  own  parts,  as  space  is  measured  by  repetition  of 
inches,  and  time  by  repetition  of  minutes.  Causes  may 
be  greater  or  less ;  as,  for  instance,  the  force  of  a  man  is 
greater  than  the  force  of  a  child.  But  how  much  is  the 
one  greater  than  the  other?  How  are  we  to  compare 
the  abstract  conception,  force,  in  such  cases  as  these  ? 

To  this  the  obvious  and  only  answer  is,  that  we  must 
compare  causes  by  means  of  their  effects ;  that  we  must 
compare  force  by  something  which  force  can  do.  The 


172         PHILOSOPHY    OF   THE   MECHANICAL    SCIENCES. 

child  can  lift  one  fagot;  the  man  can  lift  ten  such 
fagots :  we  have  here  a  means  of  comparison.  And 
whether  or  not  the  rule  is  to  be  applied  in  this  manner, 
that  is,  by  the  number  of  the  things  operated  on,  (a  ques- 
tion which  we  shall  have  to  consider  hereafter,)  it  is  clear 
that  this  form  of  rule,  namely,  a  reference  to  some  effect 
or  other  as  our  measure,  is  the  right,  because  the  only 
possible  form.  The  cause  determines  the  effect.  The 
cause  being  the  same,  the  effect  must  be  same.  The 
connexion  of  the  two  is  governed  by  a  fixed  and  invio- 
lable rule.  It  admits  of  no  ambiguity.  Every  degree  of 
intensity  in  the  cause  has  some  peculiar  modification  of 
the  effect  corresponding  to  it.  Hence  the  effect  is  an 
unfailing  index  of  the  amount  of  the  cause ;  and  if  it  be 
a  measurable  effect,  gives  a  measure  of  the  cause.  We 
can  have  no  other  measure ;  but  we  need  no  other,  for 
this  is  exact,  sufficient,  and  complete. 

It  may  be  said,  that  various  effects  are  produced  by 
the  same  cause.  The  sun's  heat  melts  wax  and  expands 
quicksilver.  The  force  of  gravity  causes  bodies  to  move 
downwards  if  they  are  free,  and  to  press  down  upon  their 
supports  if  they  are  supported.  Which  of  the  effects  is 
to  be  taken  as  the  measure  of  heat  or  of  gravity  in  these 
cases  ?  To  this  we  reply,  that  if  we  had  merely  different 
states  of  the  same  cause  to  compare,  any  of  the  effects 
might  be  taken.  The  sun's  heat  on  different  days  might 
be  measured  by  the  expansion  of  quicksilver,  or  by  the 
quantity  of  wax  melted.  The  force  of  gravity,  if  it  were 
different  at  different  places,  might  be  measured  by  the 
spaces  through  which  a  given  weight  would  bend  an  elastic 
support,  or  by  the  spaces  through  which  a  body  would 
fall  in  a  given  time.  All  these  measures  are  consistent 
with  the  general  character  of  our  idea  of  cause. 

4.  Limitation  of  the  Second  Axiom. — But  there  may 
be  circumstances  in  the  nature  of  the  case  which  may 


AXIOMS  WHICH    RELATE   TO    THE    IDEA    OF    CAUSE.      173 

further  determine  the  kind  of  effect  which  we  must  take 
for  the  measure  of  the  cause.     For  example,  if  causes  are 
conceived  to  be  of  such  a  nature  as  to  be  capable  of 
addition,  the  effects  taken  as  their  measure  must  conform 
to    this    condition.      This   is   the  case  with  mechanical 
causes.     The  weights  of  two  bodies  are  the  causes  of  the 
pressure  which  they  exert  downwards ;  and  these  weights 
are  capable  of  addition.     The  weight  of  the  two  is  the 
sum  of  the  weight  of  each.     We  are  therefore  not  at 
liberty  to  say  that  weights  shall  be  measured  by  the 
spaces  through  which  they  bend  a  certain  elastic  support, 
except  we  have  first  ascertained  that  the  whole  weight 
bends  it  through  a  space  equal  to  the  sum  of  the  inflec- 
tions produced  by  the  separate  weights.     Without  this 
precaution,  we  might  obtain  inconsistent  results.     Two 
weights,  each  of  the  magnitude  3  as  measured  by  their 
effects,  might,  if  we  took  the  inflections  for  the  effects, 
be  together  equal  to  5  or  to  7  by  the  same  kind  of  mea- 
surement.    For  the  inflection  produced  by  two  weights 
of  3  might,  for  aught  we  can  see  beforehand,  be  more 
or  less  than  twice  as  great  as  the  inflection  produced  by 
one  weight  of  3.     That  forces  are  capable  of  addition,  is 
a  condition  which  limits,  and,  as  we  shall  see,  rigorously 
fixes,  the  kind  of  effects  which  are  to  be  taken  as  their 
measures. 

Causes  which  are  thus  capable  of  addition  are  to 
be  measured  by  the  repeated  addition  of  equal  quantities. 
Two  such  causes  are  equal  to  each  other  when  they  pro- 
duce exactly  the  same  effect.  So  far  our  axiom  is  applied 
directly.  But  these  two  causes  can  be  added  together; 
and  being  thus  added,  they  are  double  of  one  of  them ; 
and  the  cause  composed  by  addition  of  three  such,  is 
three  times  as  great  as  the  first ;  and  so  on  for  any  mea- 
sure whatever.  By  this  means,  and  by  this  means  only, 
we  have  a  complete  and  consistent  measure  of  those 


174         PHILOSOPHY    OF   THE   MECHANICAL   SCIENCES. 

causes  which  are  so  conceived  as  to  be  subject  to  this 
condition  of  being  added  and  multiplied. 

Causes  are,  in  the  present  chapter,  to  be  understood 
in  the  widest  sense  of  the  term ;  and  the  axiom  now 
under  our  consideration  applies  to  them,  whenever  they 
are  of  such  a  nature  as  to  admit  of  any  measure  at  all. 
But  the  cases  which  we  have  more  particularly  in  view 
are  mechanical  causes,  the  causes  of  the  motion  and  of  the 
equilibrium  of  bodies.     In  these  cases,  forces  are  con- 
ceived as  capable  of  addition ;  and  what  has  been  said  of 
the  measure  of  causes  in  such  cases,  applies  peculiarly  to 
mechanical  forces.     Two  weights,  placed  together,  may 
be  considered  as  a  single  weight,  equal  to  the  sum  of  the 
two.     Two  pressures,  pushing  a  body  in  the  same  direc- 
tion at  the  same  point,  are  identical  in  all  respects  with 
some  single  pressure,  their  sum,  pushing  in  like  manner; 
and  this  is  true  whether  or  not  they  put  the  body  in 
motion.     In  the  cases  of  mechanical  forces,  therefore,  we 
take  some  certain  effect,  velocity  generated  or  weight 
supported,  which  may  fix  the  unit  of  force ;  and  we  then 
measure  all  other  forces  by  the  successive  repetition  of 
this  unit,  as  we  measure  all  spaces  by  the  successive  repe- 
tition of  our  unit  of  lineal  measure. 

But  these  steps  in  the  formation  of  the  science  of 
Mechanics  will  be  further  explained,  when  we  come  to 
follow  our  axioms  concerning  cause  into  their  application 
in  that  science.  At  present  we  have,  perhaps,  sufficiently 
explained  the  axiom  that  causes  are  measured  by  their 
effects,  and  we  now  proceed  to  a  third  axiom,  also  of 
great  importance. 

5.  Third  Axiom.  Reaction  is  equal  and  opposite  to 
Action. 

In  the  case  of  mechanical  forces,  the  action  of  a 
cause  often  takes  place  by  an  operation  of  one  body 
upon  another ;  and  in  this  case,  the  action  is  always  and 


AXIOMS  WHICH   RELATE   TO   THE    IDEA   OF   CAUSE.     175 

inevitably  accompanied  by  an  opposite  action.  If  I  press 
a  stone  with  my  hand,  the  stone  presses  my  hand  in 
return.  If  one  ball  strike  another  and  put  it  in  motion, 
the  second  ball  diminishes  the  motion  of  the  first.  In 
these  cases  the  operation  is  mutual ;  the  Action  is  accom- 
panied by  a  Reaction.  And  in  all  such  cases  the  Reaction 
is  a  force  of  exactly  of  the  same  nature  as  the  Action, 
exerted  in  an  opposite  direction.  A  pressure  exerted 
upon  a  body  at  rest  is  resisted  and  balanced  by  another 
pressure :  when  the  pressure  of  one  body  puts  another 
in  motion,  the  body,  though  it  yields  to  the  force,  never- 
theless exerts  upon  the  pressing  body  a  force  like  that 
which  it  suffers. 

Now  the  axiom  asserts  further,  that  this  Reaction  is 
equal,  as  well  as  opposite,  to  the  Action.    For  the  Reaction 
is  an  effect  of  the  Action,  and  is  determined  by  it.     And 
since  the  two,  Action  and  Reaction,  are  forces  of  the  same 
nature,  each  may  be  considered  as  cause  and  as  effect ; 
and  they  must,  therefore,   determine  each    other  by  a 
common  rule.     But  this  consideration  leads  necessarily 
to  their  equality:  for  since  the  rule  is  mutual,  if  we  could 
for  an  instant  suppose  the  Reaction  to  be  less  than  the 
Action,  we  must,  by  the  same  rule,  suppose  the  Action  to 
be  less  than  the  Reaction.      And  thus  Action  and  Reac- 
tion, in  every  such  case,  are  rigorously  equal  to  each  other. 
It  is  easily  seen  that  this  axiom  is  not  a  proposition 
which  is,  or  can  be,  proved  by  experience ;  but  that  its 
truth  is  anterior  to  special  observation,  and  depends  on 
our  conception  of  Action  and  Reaction.     Like  our  other 
axioms,  this  has  its  source  in  an  Idea ;  namely,  the  Idea 
of  Cause,  under  that  particular  condition  in  which  cause 
and   effect  are  mutual.      The  necessary    and   universal 
truth  which  we   cannot   help   ascribing  to  the  axiom, 
shows  that  it  is  not  derived  from  the  stores  of  experi- 
ence, which  can  never  contain  truths  of  this  character. 


170         PHILOSOPHY    OF   THE   MECHANICAL    SCIENCES. 

Accordingly,  it  was  asserted  with  equal  confidence  and 
generality  by  those  who  did  not  refer  to  experience  for 
their  principles,  and  by  those  who  did.  Leonicus 
Tomseus,  a  commentator  of  Aristotle,  whose  work  was 
published  in  1552,  and  therefore  at  a  period  when  no 
right  opinions  concerning  mechanical  reaction  were 
current,  at  least  in  his  school,  says,  in  his  remarks  on  the 
Author's  Questions  concerning  the  communication  of 
motion,  that  "  Reaction  is  equal  and  contrary  to  Action." 
The  same  principle  was  taken  for  granted  by  all  parties, 
in  all  the  controversies  concerning  the  proper  measure  of 
force,  of  which  we  shall  have  to  speak :  and  would  be 
rigorously  true,  as  a  law  of  motion,  whichever  of  the 
rival  interpretations  of  the  measure  of  the  term  "Action" 
we  were  to  take. 

6.  Extent  of  the  Third  Axiom. — It  may  naturally  be 
asked  whether  this  third  axiom  respecting  causation 
extends  to  any  other  cases  than  those  of  mechanical 
action,  since  the  notion  of  cause  in  general  has  certainly 
a  much  wider  extent.  For  instance,  when  a  hot  body 
heats  a  cold  one,  is  there  necessarily  an  equal  reaction  of 
the  second  body  upon  the  first  ?  Does  the  snowball  cool 
the  boy's  hand  exactly  as  much  as  the  hand  heats  the 
snow?  To  this  we  reply,  that,  in  every  case  in  which 
one  body  acts  upon  another  by  its  physical  qualities,  there 
must  be  some  reaction.  No  body  can  affect  another 
without  being  itself  also  affected.  But  in  any  physical 
change  the  action  exerted  is  an  abstract  term  which  may 
be  variously  understood.  The  hot  hand  may  melt  a  cold 
body,  or  may  warm  it :  which  kind  of  effect  is  to  be  taken 
as  action?  This  remains  to  be  determined  by  other 
considerations. 

In  all  cases  of  physical  change  produced  by  one  body 
in  another,  it  is  generally  possible  to  assume  such  a 
meaning  of  action,  that  the  reaction  shall  be  of  the  same 


AXIOMS  WHICH    RELATE   TO    THE   IDEA    OF    CAUSE.      177 

nature  as  the  action ;  and  when  this  is  done,  the  third 
axiom  of  causation,  that  reaction  is  equal  to  action,  is 
universally  true.  Thus  if  a  hot  body  heat  a  cold  one,  the 
change  may  be  conceived  as  the  transfer  of  a  certain  sub- 
stance, heat  or  caloric,  from  the  first  body  to  the  second. 
On  this  supposition,  the  first  body  loses  just  as  much 
heat  as  the  other  gains ;  action  and  reaction  are  equal. 
But  if  the  reaction  be  of  a  different  kind  to  the  action 
we  can  no  longer  apply  the  axiom.  If  a  hot  body  melt 
a  cold  one,  the  latter  cools  the  former:  here,  then,  is 
reaction;  but  so  long  as  the  action  and  reaction  are 
stated  in  this  form,  we  cannot  assert  any  equality  between 
them. 

In  treating  of  the  secondary  mechanical  sciences,  we 
shall  see  further  in  what  way  we  may  conceive  the  phy- 
sical action  of  one  body  upon  another,  so  that  the  same 
axioms  which  are  the  basis  of  the  science  of  Mechanics  shall 
apply  to  changes  not  at  first  sight  manifestly  mechanical. 

The  three  axioms  of  causation  which  we  have  now 
stated  are  the  fundamental  maxims  of  all  reasoning  con- 
cerning causes  as  to  their  quantities;  and  it  will  be 
shown  in  the  sequel  that  these  axioms  form  the  basis  of 
the  science  of  Mechanics,  determining  its  form,  extent, 
and  certainty.  We  must,  however,  in  the  first  place, 
consider  how  we  acquire  those  conceptions  upon  which 
the  axioms  now  established  are  to  be  employed. 


CHAPTER  V. 

OF  THE  ORIGIN  OF  OUR  CONCEPTIONS  OF  FORCE 
AND  MATTER. 

1.  Force. — When  the  faculties  of  observation  and 
thought  are  developed  in  man,  the  idea  of  causation  is 
applied  to  those  changes  which  we  see  and  feel  in  the 

VOL.  I.  N 


178        PHILOSOPHY   OF   THE   MECHANICAL    SCIENCES. 

state  of  rest  and  motion  of  bodies  around  us.  And 
when  our  abstract  conceptions  are  thus  formed  and  named, 
we  become  possessed  of  the  term  Force,  to  denote  that 
property  which  is  the  cause  of  motion  produced,  changed, 
or  prevented.  This  conception  is,  it  would  seem,  mainly 
and  primarily  suggested  by  our  consciousness  of  the 
exertions  by  which  we  put  bodies  in  motion.  The  Latin 
and  Greek  words  for  force,  vis,  Fb,  were  probably,  like  all 
abstract  terms,  derived  at  first  from  some  sensible  object. 
The  original  meaning  of  the  Greek  word  was  a  muscle  or 
tendon.  Its  first  application  as  an  abstract  term  is  accord- 
ingly to  muscular  force. 

Aevrepos  avr  Alas  TTO\V  {j.ei£ova  \aav  deipas 
TJK  fmdwfja-as,  eVcpfure  de  FIN'  airikfQpov. 

Then  Ajax  a  far  heavier  stone  upheaved, 
He  whirled  it,  and  impressing  Force  intense 
Upon  the  mass,  dismist  it. 

The  property  by  which  bodies  affect  each  other's 
motions,  was  naturally  likened  to  that  energy  which  we 
exert  upon  them  with  similar  effect :  and  thus  the  labour- 
ing horse,  the  rushing  torrent,  the  descending  weight,  the 
elastic  bow,  were  said  to  exert  force.  Homer*  speaks 
of  the  force  of  the  river,  Fls  7rora/*oto ;  and  Hesiodf  of 
the  force  of  the  north  wind,  Fls-  ave^ov  fiopeao. 

Thus  man's  general  notion  of  force  was  probably  first 
suggested  by  his  muscular  exertions,  that  is,  by  an  act 
depending  upon  that  muscular  sense,  to  which,  as  we 
have  already  seen,  the  perception  of  space  is  mainly  due, 
And  this  being  the  case,  it  will  be  easily  understood  that 
the  Direction  of  the  force  thus  exerted  is  perceived  by 
the  muscular  sense,  at  the  same  time  that  the  force  itself 
is  perceived ;  and  that  the  direction  of  any  other  force  is 
understood  by  comparison  with  force  which  man  must 
exert  to  produce  the  same  effect,  in  the  same  manner  as 
force  itself  is  so  understood. 

*  II  xxi.  t  Op.  ft  D. 


ORIGIN  OF  CONCEPTIONS  OF  FORCE  AND  MATTER.       179 

This  abstract  notion  of  Force  long  remained  in  a  very 
vague  and  obscure  condition,  as  may  be  seen  by  referring 
to  the  History  for  the  failures  of  attempts  at  a  science  of 
force  and  motion,  made  by  the  ancients  and  their  com- 
mentators in  the  middle  ages.  By  degrees,  in  modern 
times,  we  see  the  scientific  faculty  revive.  The  concep- 
tion of  force  becomes  so  far  distinct  and  precise  that  it 
can  be  reasoned  upon  in  a  consistent  manner,  with  demon- 
strated consequences ;  and  a  genuine  science  of  Mecha- 
nics comes  into  existence.  The  foundations  of  this 
science  are  to  be  found  in  the  Axioms  concerning  causa- 
tion which  we  have  already  stated ;  these  axioms  being 
interpreted  and  fixed  in  their  application  by  a  constant 
reference  to  observed  facts,  as  we  shall  show.  But  we 
must,  in  the  first  place,  consider  further  those  primary 
processes  of  observation  by  which  we  acquire  the  first 
materials  of  thought  on  such  subjects. 

2.  Matter. — The  conception  of  Force,  as  we  have  said, 
arises  with  our  consciousness  of  our  own  muscular  exer- 
tions. But  we  cannot  imagine  such  exertions  without 
also  imagining  some  bodily  substance  against  which  they 
are  exercised.  If  we  press,  we  press  something :  if  we 
thrust  or  throw,  there  must  be  something  to  resist  the 
thrust  or  to  receive  the  impulse.  Without  body,  mus- 
cular force  cannot  be  exerted,  and  force  in  general  is  not 
conceivable. 

Thus  Force  cannot  exist  without  Body  on  which  it 
acts.  The  two  conceptions,  Force  and  Matter,  are  coex- 
istent and  correlative.  Force  implies  resistance;  and 
the  force  is  effective  only  when  the  resistance  is  called 
into  play.  If  we  grasp  a  stone,  we  have  no  hold  of  it 
till  the  closing  of  the  hand  is  resisted  by  the  solid  texture 
of  the  stone.  If  we  push  open  a  gate,  we  must  sur- 
mount the  opposition  which  it  exerts  while  turning 
on  its  hinges.  However  slight  the  resistance  be,  there 

N  2 


180        PHILOSOPHY    OF   THE   MECHANICAL    SCIENCES. 

must  be  some  resistance,  or  there  would  be  no  force. 
If  we  imagine  a  state  of  things  in  which  objects  do  not 
resist  our  touch,  they  must  also  cease  to  be  influenced  by 
our  strength.  Such  a  state  of  things  we  sometimes 
imagine  in  our  dreams ;  and  such  are  the  poetical  pictures 
of  the  regions  inhabited  by  disembodied  spirits.  In 
these,  the  figures  which  appear  are  conspicuous  to  the 
eye,  but  impalpable  like  shadow  or  smoke ;  and  as  they 
do  not  resist  the  corporeal  impressions,  so  neither  do 
they  obey  them.  The  spectator  tries  in  vain  to  strike 
or  to  grasp  them. 

Et  ni  cana  vates  tenues  sine  corpore  vitas 
Admoneat  volitare  cava  sub  imagine  formae, 
Irruafc  ac  frustra  ferro  diverberet  umbras. 

The  Sibyl  warns  him  that  there  round  him  fly 
Bodiless  things,  but  substance  to  the  eye; 
Else  had  he  pierced  those  shapes  with  life-like  face, 
And  smitten,  fierce,  the  unresisting  space. 

Neque  ilium 

Prensantem  nequicquam  umbras  et  multa  volentem 
Dicere,  preterea  vidit. 

He  grasps  her  form,  and  clutches  but  the  shade. 

Such  may  be  the  circumstances  of  the  unreal  world  of 
dreams,  or  of  poetical  fancies  approaching  to  dreams : 
for  in  these  worlds  our  imaginary  perceptions  are  bound 
by  no  rigid  conditions  of  force  and  reaction.  In  such 
cases,  the  mind  casts  off  the  empire  of  the  idea  of  cause, 
as  it  casts  off  even  the  still  more  familiar  sway  of  the 
ideas  of  space  and  time.  But  the  character  of  the 
material  world  in  which  we  live  when  awake  is,  that  we 
have  at  every  instant  and  at  every  place,  force  operating 
on  matter  and  matter  resisting  force. 

3.  Solidity. — From  our  consciousness  of  muscular 
exertion,  we  derive,  as  we  have  seen,  the  conception  of 
force,  and  with  that  also  the  conception  of  matter.  We 
have  already  shown,  in  a  former  chapter,  that  the  same 


ORIGIN  OF  CONCEPTIONS  OF  FORCE  AND  MATTER.   181 

part  of  our  frame,  the  muscular  system,  is  the  organ  by 
which  we  perceive  extension  and  the  relations  of  space. 
Thus  the  same  organ  gives  us  the  perception  of  body  as 
resisting  force,  and  as  occupying  space  ;  and  by  combin- 
ing these  conditions  we  have  the  conception  of  solid 
extended  bodies.  In  reality,  this  resistance  is  inevitably 
presented  to  our  notice  in  the  very  facts  from  which  we 
collect  the  notion  of  extension.  For  the  action  of  the 
hand  and  arm  by  which  we  follow  the  forms  of  objects, 
implies  that  we  apply  our  fingers  to  their  surface ;  and 
we  are  stopped  there  by  the  resistance  which  the  body 
offers.  This  resistance  is  precisely  that  which  is  requisite 
in  order  to  make  us  conscious  of  our  muscular  effort*. 
Neither  touch,  nor  any  other  mere  passive  sensation, 
could  produce  the  perception  of  extent,  as  we  have 
already  urged  :  nor  could  the  muscular  sense  lead  to  such 
a  perception,  except  the  extension  of  the  muscles  were 
felt  to  be  resisted.  And  thus  the  perception  of  resistance 
enters  the  mind  along  with  the  perception  of  extended 
bodies.  All  the  objects  with  which  we  have  to  do  are 
not  only  extended  but  solid. 

This  sense  of  the  term  solidity,  (the  general  property 
of  all  matter,)  is  different  to  that  in  which  we  oppose 
solidity  to  fluidity.  We  may  avoid  ambiguity  by  op- 
posing rigid  to  fluid  bodies.  By  solid  bodies,  as  wre  now 
speak  of  them,  we  mean  only  such  as  resist  the  pressure 
which  we  exert,  so  long  as  their  parts  continue  in  their 
places.  By  fluid  bodies,  we  mean  those  whose  parts  are, 
by  a  slight  pressure,  removed  out  of  their  places.  A  drop 
of  water  ceases  to  prevent  the  contact  of  our  two  hands, 
not  by  ceasing  to  have  solidity  in  this  sense,  but  by  being 
thrust  out  of  the  way.  If  it  could  remain  in  its  place, 
it  could  not  cease  to  exercise  its  resistance  to  our  pres- 
sure, except  by  ceasing  to  be  matter  altogether. 

*  BROWN'S  Lectures,  i.,  466. 


182       PHILOSOPHY   OF  THE   MECHANICAL   SCIENCES. 

The  perception  of  solidity,  like  the  perception  of 
extension,  implies  an  act  of  the  mind,  as  well  as  an 
impression  of  the  senses :  as  the  perception  of  extension 
implies  the  idea  of  space,  so  the  perception  of  solidity 
implies  the  idea  of  action  and  reaction.  That  an  idea 
is  involved  in  our  knowledge  on  this  subject  appears,  as  in 
other  instances,  from  this  consideration,  that  the  convic- 
tions of  persons,  even  of  those  who  allow  of  no  ground  of 
knowledge  but  experience,  do  in  fact  go  far  beyond  the 
possible  limits  of  experience.  Thus  Locke  says*,  that  "the 
bodies  which  we  daily  handle  hinder  by  an  insurmountable 
force  the  approach  of  the  parts  of  our  hands  that  press 
them."  Now  it  is  manifest  that  our  observation  can 
never  go  to  this  length.  By  our  senses  we  can  only 
perceive  that  bodies  resist  the  greatest  actual  forces  that 
we  exert  upon  them.  But  our  conception  of  force  carries 
us  further:  and  since,  so  long  as  the  body  is  there  to 
receive  the  action  of  the  force,  it  must  suffer  the  whole 
of  that  action,  and  must  react  as  much  as  it  suffers :  it 
is  therefore  true,  that  so  long  as  the  body  remains  there, 
the  force  which  is  exerted  upon  it  can  never  surmount 
the  resistance  which  the  body  exercises.  And  thus  this 
doctrine,  that  bodies  resist  the  intrusion  of  other  bodies 
by  an  insurmountable  force,  is  in  fact  a  consequence  of 
the  axiom  that  the  reaction  is  always  equal  to  the  action. 

4.  Inertia. — But  this  principle  of  the  equality  of  action 
and  reaction  appears  also  in  another  way.  Not  only 
when  we  exert  force  upon  bodies  at  rest,  but  when,  by 
our  exertions,  we  put  them  in  motion,  they  react.  If  we 
set  a  large  stone  in  motion,  the  stone  resists ;  for  the  ope- 
ration requires  an  effort.  By  increasing  the  effort,  we 
can  increase  the  effect,  that  is,  the  motion  produced ;  but 
the  resistance  still  remains.  And  the  greater  the  stone 
moved,  the  greater  is  the  effort  requisite  to  move  it. 
*  Essay,  b.  ii.,  c.  4. 


ORIGIN  OF  CONCEPTIONS  OF  FORCE  AND  MATTER.       183 

There  is,  in  every  case,  a  resistance  to  motion,  which  shows 
itself,  not  in  preventing  the  motion,  but  in  a  reciprocal 
force,  exerted  backwards  upon  the  agent  by  which  the 
motion  is  produced.  And  this  resistance  resides  in 
each  portion  of  matter,  for  it  is  increased  as  we 
add  one  portion  of  matter  to  another.  We  can  push  a 
light  boat  rapidly  through  the  water ;  but  we  may  go  on 
increasing  its  freight,  till  we  are  barely  able  to  stir  it. 
This  property  of  matter,  then,  by  which  it  resists  the  re- 
ception of  motion,  or  rather  by  which  it  reacts  and  re- 
quires an  adequate  force  in  order  that  any  motion  may 
result,  is  called  its  inertness,  or  inertia.  That  matter  has 
such  a  property,  is  a  conviction  flowing  from  that  idea  of 
a  reaction  equal  and  opposite  to  the  action,  which  the 
conception  of  all  force  involves.  By  what  laws  this 
inertia  depends  on  the  magnitude,  form,  and  material  of 
the  body,  must  be  the  subject  of  our  consideration  here- 
after. But  that  matter  has  this  inertia,  in  virtue  of 
which,  as  the  matter  is  greater,  the  velocity  which  the 
same  effort  can  communicate  to  it  is  less,  is  a  principle 
inseparable  from  the  notion  of  matter  itself. 

Hermann  says  that  Kepler  first  introduced  this  "  most 
significant  word"  inertia.  Whether  it  is  to  be  found  in 
earlier  writers  I  know  not ;  Kepler  certainly  does  use  it 
familiarly  in  those  attempts  to  assign  physical  reasons  for 
the  motions  of  the  planets  which  were  among  the  main 
occasions  of  the  discovery  of  the  true  laws  of  mechanics. 
He  assumes  the  slowness  of  the  motions  of  the  planets 
to  increase,  (other  causes  remaining  the  same,)  as  the 
inertia  increases ;  and  though,  even  in  this  assumption, 
there  is  an  error  involved,  (if  we  adopt  that  interpreta- 
tion of  the  term  inertia  to  which  subsequent  researches 
led,)  the  introduction  of  such  a  word  was  one  step  in 
determining  and  expressing  those  laws  of  motion  which 
depend  on  the  fundamental  principle  of  the  equality  of 
action  and  reaction. 


184        PHILOSOPHY   OF   THE   MECHANICAL   SCIENCES. 

5.  We  have  thus  seen,  I  trust  in  a  satisfactory 
manner,  the  origin  of  our  conceptions  of  Force,  Matter, 
Solidity,  and  Inertness.  It  has  appeared  that  the  organ 
by  which  we  obtain  such  conceptions  is  that  very  mus- 
cular frame,  which  is  the  main  instrument  of  our  percep- 
tions of  space ;  but  that,  besides  bodily  sensations,  these 
ideal  conceptions,  like  all  the  others  which  we  have 
hitherto  considered,  involve  also  an  habitual  activity  of 
the  mind,  giving  to  our  sensations  a  meaning  which  they 
could  not  otherwise  possess.  And  among  the  ideas  thus 
brought  into  play,  is  an  idea  of  action  with  an  equal  and 
opposite  reaction,  which  forms  a  foundation  for  universal 
truths  to  be  hereafter  established  respecting  the  concep- 
tions thus  obtained. 

We  must  now  endeavour  to  trace  in  what  manner 
these  fundamental  principles  and  conceptions  are  un- 
folded by  means  of  observation  and  reasoning,  till  they 
become  an  extensive  yet  indisputable  science. 


CHAPTER  VI. 

OF  THE  ESTABLISHMENT  OF  THE  PRINCIPLES 
OF  STATICS. 

1.  Object  of  the  Chapter. — In  the  present  and  the  suc- 
ceeding chapters  we  have  to  show  how  the  general  axioms 
of  Causation  enable  us  to  construct  the  science  of  Me- 
chanics. We  have  to  consider  these  axioms  as  moulding 
themselves,  in  the  first  place,  into  certain  fundamental 
mechanical  principles,  which  are  of  evident  and  necessary 
truth  in  virtue  of  their  dependence  upon  the  general 
axioms  of  Causation ;  and  thus  as  forming  a  foundation 
for  the  whole  structure  of  the  science ;  a  system  of  truths 
no  less  necessary  than  the  fundamental  principles,  because 
derived  from  these  by  rigorous  demonstration. 


ESTABLISHMENT  OF  THE  PRINCIPLES  OF  STATICS.      185 

This  account  of  the  construction  of  the  science  of 
Mechanics,  however  generally  treated,  cannot  be  other- 
wise than  technical  in  its  details,  and  will  probably  be 
imperfectly  understood  by  any  one  not  acquainted  with 
Mechanics  as  a  mathematical  science. 

I  cannot  omit  this  portion  of  my  survey  without 
rendering  my  work  incomplete ;  but  I  may  remark  that 
the  main  purpose  of  it  is  to  prove,  in  a  more  particular 
manner,  what  I  have  already  declared  in  general,  that 
there  are  in  Mechanics  no  less  than  in  Geometry,  funda- 
mental principles  of  axiomatic  evidence  and  necessity; 
— that  these  principles  derive  their  axiomatic  character 
from  the  Idea  which  they  involve,  namely  the  Idea  of 
Cause  ; — and  that  through  the  combination  of  principles 
of  this  kind,  the  whole  science  of  Mechanics,  including  its 
most  complex  and  remote  results,  exists  as  a  body  of  solid 
and  universal  truths. 

2.  Statics  and  Dynamics. — We  must   first  turn  our 
attention  to  a  technical  distinction  of  Mechanics  into  two 
portions,  according  as  the  forces  about  which  we  reason 
produce  rest,   or  motion ;  the  former  portion  is  termed 
Statics,  the  latter  Dynamics.     If  a  stone  fall,  or  a  weight 
put  a  machine  in  motion,  the  problem  belongs  to  Dy- 
namics; but  if  the   stone   rest  upon  the  ground,   or  a 
weight  be  merely  supported  by  a  machine,  without  being 
raised  higher,  the  question  is  one  of  Statics. 

3.  Equilibrium. — In  Statics,  forces  balance  each  other, 
or  keep   each  other  in  equilibrium.     And  forces  which 
directly  balance  each  other,  or  keep  each  other  in  equili- 
brium, are  necessarily  and  manifestly  equal.     If  we  see 
two  boys  pull  at  two  ends  of  a  rope  so  that  neither  of 
them  in  the  smallest  degree  prevails  over  the  other,  we 
have  a  case  in  which  two  forces  are  in  equilibrium.     The 
two  forces  are  evidently  equal,  and  are  a  statical  exem- 
plification of  action  and  reaction,  such  as  are  spoken  of 


186          PHILOSOPHY  OF  THE  MECHANICAL  SCIENCES. 

in  the  third  axiom  concerning  causes.  Now  the  same 
exemplification  occurs  in  every  case  of  equilibrium.  No 
point  or  body  can  be  kept  at  rest  except  in  virtue  of 
opposing  forces  acting  upon  it ;  and  these  forces  must 
always  be  equal  in  their  opposite  effect.  When  a  stone 
lies  on  the  floor,  the  weight  of  the  stone  downwards  is 
opposed  and  balanced  by  an  equal  pressure  of  the  floor 
upwards.  If  the  stone  rests  on  a  slope,  its  tendency  to 
slide  is  counteracted  by  some  equal  and  opposite  force, 
arising,  it  may  be,  from  the  resistance  which  the  sloping 
ground  opposes  to  any  motion  along  its  surface.  Every 
case  of  rest  is  a  case  of  equilibrium  :  every  case  of  equi- 
librium is  a  case  of  equal  and  opposite  forces. 

The  most  complex  frame-work  on  which  weights  are 
supported,  as  the  roof  of  a  building,  or  the  cordage  of  a 
machine,  are  still  examples  of  equilibrium.  In  such 
cases  we  may  have  many  forces  all  combining  to  balance 
each  other ;  and  the  equilibrium  will  depend  on  various 
conditions  of  direction  and  magnitude  among  the  forces. 
And  in  order  to  understand  what  are  these  conditions,  we 
must  ask,  in  the  first  place,  what  we  understand  by  the 
magnitude  of  such  forces; — what  is  the  measure  of 
statical  forces. 

4.  Measure  of  Statical  Forces. — At  first  we  might 
expect,  perhaps,  that  since  statical  forces  come  under  the 
general  notion  of  Cause,  the  mode  of  measuring  them 
would  be  derived  from  the  second  axiom  of  Causation, 
that  causes  are  measured  by  their  effects.  But  we  find 
that  the  application  of  this  axiom  is  controlled  by  the 
limitation  which  we  noticed,  after  stating  that  axiom ; 
namely,  the  condition  that  the  causes  shall  be  capable  of 
addition.  Further,  as  we  have  seen,  a  statical  force  pro- 
duces no  other  effect  than  this,  that  it  balances  some  other 
statical  force ;  and  hence  the  measure  of  statical  forces  is 
necessarily  dependent  upon  their  balancing,  that  is,  upon 
the  equality  of  action  and  reaction. 


ESTABLISHMENT  OF  THE  PRINCIPLES  OF  STATICS.        187 

That  statical  forces  are  capable  of  addition  is  involved 
in  our  conception  of  such  forces.  When  two  men  pull 
at  a  rope  in  the  same  direction,  the  forces  which  they 
exert  are  added  together.  When  two  heavy  bodies  are 
put  into  a  basket  suspended  by  a  string,  their  weights  are 
added,  and  the  sum  is  supported  by  the  string. 

Combining  these  considerations,  it  will  appear  that 
the  measure  of  statical  forces  is  necessarily  given  at  once 
by  the  fundamental  principle  of  the  equality  of  action 
and  reaction.  Since  two  opposite  forces  which  balance 
each  other  are  equal,  each  force  is  measured  by  that 
which  it  balances ;  and  since  forces  are  capable  of  addi- 
tion, a  force  of  any  magnitude  is  measured  by  adding  to- 
gether a  proper  number  of  such  equal  forces.  Thus  a  heavy 
body  which,  appended  to  some  certain  elastic  branch  of  a 
tree,  would  bend  it  down  through  one  inch,  may  be  taken 
as  a  unit  of  weight.  Then  if  we  remove  this  first  body, 
and  find  a  second  heavy  body  which  will  also  bend  the 
branch  through  the  same  space,  this  is  also  a  unit  of 
weight ;  and  in  like  manner  we  might  go  on  to  a  third 
and  a  fourth  equal  body ;  and  adding  together  the  two^ 
or  the  three,  or  the  four  heavy  bodies,  we  have  a  force 
twice,  or  three  times,  or  four  times  the  unit  of  weight. 
And  with  such  a  collection  of  heavy  bodies,  or  weights,  we 
can  readily  measure  all  other  forces ;  for  the  same  prin- 
ciple of  the  equality  of  action  and  reaction  leads  at  once 
to  this  maxim,  that  any  statical  force  is  measured  by  the 
weight  which  it  would  support. 

As  has  been  said,  it  might  at  first  have  been  supposed 
that  we  should  have  to  apply,  in  this  case,  the  axiom  that 
causes  are  measured  by  their  effects  in  another  manner ; 
that  thus,  if  that  body  were  a  unit  of  weight  which  bent 
the  bough  of  a  tree  through  one  inch,  that  body  would  be 
two  units  which  bent  it  through  two  inches,  and  so  on. 
But,  as  we  have  already  stated,  the  measures  of  weight 


188  PHILOSOPHY  OF  THE  MECHANICAL  SCIENCES, 

must  be  subject  to  this  condition,  that  they  are  susceptible 
of  being  added :  and  therefore  we  cannot  take  the  deflex- 
ion of  the  bough  for  our  measure,  till  we  have  ascertained, 
that  which  experience  alone  can  teach  us,  that  under  the 
burden  of  two  equal  weights,  the  deflexion  will  be  twice  as 
great  as  it  is  with  one  weight,  which  is  not  true,  or  at 
least  is  neither  obviously  nor  necessarily  true.  In  this, 
as  in  all  other  cases,  although  causes  must  be  measured 
by  their  effects,  we  learn  from  experience  only  how  the 
effects  are  to  be  interpreted,  so  as  to  give  a  true  and 
consistent  measure. 

With  regard,  however,  to  the  measure  of  statical 
force,  and  of  weight,  no  difficulty  really  occurred  to  phi- 
losophers from  the  time  when  they  first  began  to  specu- 
late on  such  subjects ;  for  it  was  easily  seen  that  if  we 
take  any  uniform  material,  as  wood,  or  stone,  or  iron,  por- 
tions of  this  which  are  geometrically  equal,  must  also  be 
equal  in  statical  effect ;  for  this  was  implied  in  the  very 
hypothesis  of  a  uniform  material.  And  a  body  ten  times 
as  large  as  another  of  the  same  substance,  will  be  of  ten 
times  the  weight.  But  before  men  could  establish  by 
reasoning  the  conditions  under  which  weights  would  be  in 
equilibrium,  some  other  principles  were  needed  in  addi- 
tion to  the  mere  measure  of  forces.  The  principles  in- 
troduced for  this  purpose  still  resulted  from  the  concep- 
tion of  equal  action  and  reaction ;  but  it  required  no 
small  clearness  of  thought  to  select  them  rightly,  and  to 
employ  them  successfully.  This,  however,  was  done,  to  a 
certain  extent,  by  the  Greeks ;  and  the  treatise  of  Archi- 
medes On  the  Centre  of  Gravity,  is  founded  on  principles 
which  may  still  be  considered  as  the  genuine  basis  of  sta- 
tical reasoning.  I  shall  make  a  few  remarks  on  the  most 
important  principle  among  those  which  Archimedes  thus 
employs. 

5.  2he   Centre  of  Gravity. — The  most  important  of 


ESTABLISHMENT  OF  THE  PRINCIPLES  OF  STATICS.       189 

the  principles  which  enter  into  the  demonstration  of 
Archimedes  is  this:  that  "Every  body  has  a  centre  of 
gravity ;"  meaning  by  the  centre  of  gravity,  a  point  at 
which  the  whole  matter  of  the  body  may  be  supposed  to 
be  collected,  to  all  intents  and  purposes  of  statical 
reasoning.  This  principle  has  been  put  in  various  forms 
by  succeeding  writers :  for  instance,  it  has  been  thought 
sufficient  to  assume  a  case  much  simpler  than  the  general 
one;  and  to  assert  that  two  equal  bodies  have  their 
centre  of  gravity  in  the  point  midway  between  them.  It 
is  to  be  observed,  that  this  assertion  not  only  implies 
that  the  two  bodies  will  balance  upon  a  support  placed 
at  that  midway  point,  but  also,  that  they  will  exercise, 
upon  such  a  support,  a  pressure  equal  to  their  sum ; 
for  this  point  being  the  centre  of  gravity,  the  whole 
matter  of  the  two  bodies  may  be  conceived  to  be  col- 
lected there,  and  therefore  the  whole  weight  will  press 
there.  And  thus  the  principle  in  question  amounts  to 
this,  that  when  two  equal  heavy  bodies  are  supported  on  the 
middle  point  between  them,  the  pressure  upon  the  support  is 
equal  to  the  sum  of  the  weights  of  the  bodies. 

A  clear  understanding  of  the  nature  and  grounds  of 
this  principle  is  of  great  consequence :  for  in  it  we  have 
the  foundation  of  a  large  portion  of  the  science  of 
Mechanics.  And  if  this  principle  can  be  shown  to  be 
necessarily  true,  in  virtue  of  our  Fundamental  Ideas,  we 
can  hardly  doubt  that  there  exist  many  other  truths  of 
the  same  kind,  and  that  no  sound  view  of  the  evidence 
and  extent  of  human  knowledge  can  be  obtained,  so  long 
as  we  mistake  the  nature  of  these,  its  first  principles. 

The  above  principle,  that  the  pressure  on  the  support 
is  equal  to  the  sum  of  the  bodies  supported,  is  often 
stated  as  an  axiom  in  the  outset  of  books  on  Mechanics. 
And  this  appears  to  be  the  true  place  and  character  of 
this  principle,  in  accordance  with  the  reasonings  which 


190          PHILOSOPHY  OF  THE  MECHANICAL  SCIENCES. 

we  have  already  urged.  The  axiom  depends  upon  our 
conception  of  action  and  reaction.  That  the  two  weights 
are  supported,  implies  that  the  supporting  force  must  be 
equal  to  the  force  or  weight  supported. 

In  order  further  to  show  the  foundation  of  this 
principle,  we  may  ask  the  question :  i£  it  be  not  an 
axiom,  deriving  its  truth  from  the  fundamental  concep- 
tion of  equal  action  and  reaction,  which  equilibrium 
always  implies,  what  is  the  origin  of  its  certainty  ?  The 
principle  is  never  for  an  instant  denied  or  questioned:  it  is 
taken  for  granted,  even  before  it  is  stated.  No  one  will 
doubt  that  it  is  not  only  true,  but  true  with  the  same 
rigour  and  universality  as  the  axioms  of  Geometry.  Will 
it  be  said,  that  it  is  borrowed  from  experience  ?  Expe- 
rience could  never  prove  a  principle  to  be  universally  and 
rigorously  true.  Moreover,  when  from  experience  we 
prove  a  proposition  to  possess  great  exactness  and 
generality,  we  approach  by  degrees  to  this  proof:  the 
conviction  becomes  stronger,  the  truth  more  secure,  as 
we  accumulate  trials.  But  nothing  of  this  kind  is  the 
case  in  the  instance  before  us.  There  is  no  gradation 
from  less  to  greater  certainty; — no  hesitation  which 
precedes  confidence.  From  the  first,  we  know  that  the 
axiom  is  exactly  and  certainly  true.  In  order  to  be 
convinced  of  it,  we  do  not  require  many  trials,  but 
merely  a  clear  understanding  of  the  assertion  itself. 

But,  in  fact,  not  only  are  trials  not  necessary  to  the 
proof,  but  they  do  not  strengthen  it.  Probably  no 
one  ever  made  a  trial  for  the  purpose  of  showing  that 
the  pressure  upon  the  support  is  equal  to  the  sum  of  the 
two  weights.  Certainly  no  person  with  clear  mechanical 
conceptions  ever  wanted  such  a  trial  to  convince  him  of 
the  truth ;  or  thought  the  truth  clearer  after  the  trial 
had  been  made.  If  to  such  a  person,  an  experiment 
were  shown  which  seemed  to  contradict  the  principle,  his 


ESTABLISHMENT  OF  THE  PRINCIPLES  OF  STATICS.      191 

conclusion  would  be,  not  that  the  principle  was  doubtful, 
but  that  the  apparatus  was  out  of  order.  Nothing  can 
be  less  like  collecting  truth  from  experience. 

We  maintain,  then,  that  this  equality  of  mechanical 
action  and  reaction,  is  one  of  the  principles  which  do 
not  flow  from,  but  regulate  our  experience.  To  this 
principle,  the  facts  which  we  observe  must  conform; 
and  we  cannot  help  interpreting  them  in  such  a  manner 
that  they  shall  be  exemplifications  of  the  principle.  A 
mechanical  pressure  not  accompanied  by  an  equal  and 
opposite  pressure,  can  no  more  be  given  by  experience, 
than  two  unequal  right  angles.  With  the  supposition  of 
such  inequalities,  space  ceases  to  be  space,  force  ceases  to 
be  force,  matter  ceases  to  be  matter.  And  this  equality 
of  action  and  reaction,  considered  in  the  case  in  which 
two  bodies  are  connected  so  as  to  act  on  a  single  support, 
leads  to  the  axiom  which  we  have  stated  above,  and 
which  is  one  of  the  main  foundations  of  the  science  of 
Mechanics. 

6.  Oblique  Forces. — By  the  aid  of  this  axiom  and  a 
few  others,  the  Greeks  made  some  progress  in  the 
science  of  Statics.  But  after  a  short  advance,  they 
arrived  at  another  difficulty,  that  of  Oblique  Forces, 
which  they  never  overcame ;  and  which  no  mathematician 
mastered  till  modern  times.  The  unpublished  manuscripts 
of  Leonardo  da  Vinci,  written  in  the  fifteenth  century, 
and  the  works  of  Stevinus  and  Galileo,  in  the  sixteenth, 
are  the  places  in  which  we  find  the  first  solid  grounds  of 
reasoning  on  the  subject  of  forces  acting  obliquely  to 
each  other.  And  mathematicians,  having  thus  become 
possessed  of  all  the  mechanical  principles  which  are 
requisite  in  problems  respecting  equilibrium,  soon  framed 
a  complete  science  of  Statics.  Succeeding  writers  pre- 
sented this  science  in  forms  variously  modified;  for  it 
was  found,  in  Mechanics  as  in  Geometry,  that  various 


192          PHILOSOPHY  OP  THE  MECHANICAL  SCIENCES. 

propositions  might  be  taken  as  the  starting  points  ;  and 
that  the  collection  of  truths  which  it  was  the  mecha- 
nician's business  to  include  in  his  course,  might  be 
traversed  by  various  routes,  each  path  offering  a  series 
of  satisfactory  demonstrations.  The  fundamental  con- 
ceptions of  force  and  resistance,  like  those  of  space  and 
number,  could  be  contemplated  under  different  aspects, 
each  of  which  might  be  made  the  basis  of  axioms, 
or  of  principles  employed  as  axioms.  Hence  the 
grounds  of  the  truth  of  Statics  may  be  stated  in  various 
ways ;  and  it  would  be  a  task  of  some  length  to  examine 
all  these  completely,  and  to  trace  them  to  their  Funda- 
mental Ideas.  This  I  shall  not  undertake  here  to  do ; 
but  the  philosophical  importance  of  the  subject  makes  it 
proper  to  offer  a  few  remarks  on  some  of  the  main 
principles  involved  in  the  different  modes  of  presenting 
Statics  as  a  rigorously  demonstrated  science. 

7.  A  force  may  be  supposed  to  act  at  any  Point  of  its 
Direction. — It  has  been  stated  in  the  history  of  Mechanics*, 
that  Leonardo  da  Vinci  and  Galileo  obtained  the  true 
measure  of  the  effect  of  oblique  forces,  by  reasonings 
which  were,  in  substance,  the  same.  The  principle  of 
these  reasonings  is  that  expressed  at  the  head  of  this 
paragraph ;  and  when  we  have  a  little  accustomed  our- 
selves to  contemplate  our  conceptions  of  force,  and  its 
action  on  matter,  in  an  abstract  manner,  we  shall  have 
no  difficulty  in  assenting  to  the  principle  in  this  general 
form.  But  it  may,  perhaps,  be  more  obvious  at  first  in  a 
special  case. 

If  we  suppose  a  wheel,  moveable  about  its  axis,  and 
carrying  with  it  in  its  motion  a  weight,  (as,  for  example, 
one  of  the  wheels  by  means  of  which  the  large  bells  of  a 
church  are  rung,)  this  weight  may  be  supported  by  means 
of  a  rope  (not  passing  along  the  circumference  of  the  wheel, 

*  Hist.  Ind.  8c.,  ii.  pp.  17  and  122. 


ESTABLISHMENT  OF  THE  PRINCIPLES  OP  STATICS.      1  93 

as  is  usual  in  the  case  of  bells,)  but  fastened  to  one  of 
the  spokes  of  the  wheel.  Now  the  principle  which  is 
enunciated  above  asserts,  that  if  the  rope  pass  in  a 
straight  line  across  several  of  the  spokes  of  the  wheel,  it 
makes  no  difference  in  the  mechanical  effect  of  the  force 
applied,  for  the  purpose  of  putting  the  bell  in  motion,  to 
which  of  these  spokes  the  rope  is  fastened.  In  each  case, 
fastening  the  rope  to  the  wheel  merely  serves  to  enable 
the  force  to  produce  motion  about  the  centre;  and  so  long 
as  the  force  acts  in  the  same  line,  the  effect  is  the  same, 
at  whatever  point  of  the  rope  the  line  of  action  finishes. 

This  axiom  very  readily  aids  us  in  estimating  the 
effect  of  oblique  forces.  For  when  a  force  acts  on  one  of 
the  arms  of  a  lever  at  any  oblique  angle,  we  suppose 
another  arm  projecting  from  the  centre  of  motion,  like 
another  spoke  of  the  same  wheel,  so  situated  that  it  is 
perpendicular  to  the  force.  This  arm  we  may,  with 
Leonardo,  call  the  virtual  lever ;  for,  by  the  axiom,  we 
may  suppose  the  force  to  act  where  the  line  of  its  direction 
meets  this  arm ;  and  thus  we  reduce  the  case  to  that  in 
which  the  force  acts  perpendicularly  on  the  arm. 

The  ground  of  this  axiom  is,  that  matter,  in  Statics, 
is  necessarily  conceived  as  transmitting  force.  That  force 
can  be  transmitted  from  one  place  to  another,  by  means 
of  matter; — that  we  can  push  with  a  rod,  pull  with  a 
rope, — are  suppositions  implied  in  our  conceptions  of 
force  and  matter.  Matter  is,  as  we  have  said,  that  which 
receives  the  impression  of  force,  and  the  modes  just 
mentioned,  are  the  simplest  ways  in  which  that  impression 
operates.  And  since,  in  any  of  these  cases,  the  force 
might  be  resisted  by  a  reaction  equal  to  the  force  itself, 
the  reaction  in  each  case  would  be  equal,  and,  therefore, 
the  action  in  each  case  is  necessarily  equal ;  and  thus  the 
forces  must  be  transmitted,  from  one  point  to  another, 
without  increase  or  diminution. 

VOL.  i.  o 


194          PHILOSOPHY  OF  THE  MECHANICAL  SCIENCES. 

This  property  of  matter,  of  transmitting  the  action  of 
force,  is  of  various  kinds.  We  have  the  coherence  of  a 
rope  which  enables  us  to  pull,  and  the  rigidity  of  a  staff, 
which  enables  us  to  push  with  it  in  the  direction  of  its 
length  ;  and  again,  the  same  staff  has  a  rigidity  of  another 
kind,  in  virtue  of  which  we  can  use  it  as  a  lever ;  that  is,  a 
rigidity  to  resist  flexure,  and  to  transmit  the  force  which 
turns  a  body  round  a  fulcrum.  There  is,  further,  the 
rigidity  by  which  a  solid  body  resists  twisting.  Of  these 
kinds  of  rigidity,  the  first  is  that  to  which  our  axiom 
refers;  but  in  order  to  complete  the  list  of  the  ele- 
mentary principles  of  Statics,  we  ought  also  to  lay  down 
axioms  respecting  the  other  kinds  of  rigidity*.  These, 
however,  I  shall  not  here  state,  as  they  do  not  involve 
any  new  principle.  Like  the  one  just  considered,  they 
form  part  of  our  fundamental  conception  of  matter ;  they 
are  not  the  results  of  any  experience,  but  are  the  hypo- 
theses to  which  we  are  irresistibly  led,  when  we  would 
liberate  our  reasonings  concerning  force  and  matter  from 
a  dependence  on  the  special  results  of  experience.  We 
cannot  even  conceive  (that  is,  if  we  have  any  clear 
mechanical  conceptions  at  all)  the  force  exerted  by  the 
point  of  a  staff  and  resisting  the  force  which  we  steadily 
impress  on  the  head  of  it,  to  be  different  from  the 
impressed  force. 

8.  Forces  may  have  equivalent  Forces  substituted  for 
them.  The  Parallelogram  of  Forces. — It  has  already  been 
observed,  that  in  order  to  prove  the  doctrines  of  Statics, 
we  may  take  various  principles  as  our  starting  points, 
and  may  still  find  a  course  of  demonstration  by  which 
the  leading  propositions  belonging  to  the  subject  may 
be  established.  Thus,  instead  of  beginning  our  reason- 
ings, as  in  the  last  section  we  supposed  them  to 

*  Such  axioms  are  given  in  a  little  work  (The  Mechanical  Euclid 
which  I  published  on  the  Elements  of  Mechanics. 


ESTABLISHMENT  OF  THE  PRINCIPLES  OF  STATICS.      195 

commence,  with  the  case  in  which  forces  act  upon 
different  points  of  the  same  body  in  the  same  line  of 
force,  and  counteract  each  other  in  virtue  of  the  inter- 
vening matter  by  which  the  effect  of  force  is  transferred 
from  one  point  to  another,  we  may  suppose  different 
forces  to  act  at  the  same  point,  and  may  thus  commence 
our  reasonings  with  a  case  in  which  we  have  to  con- 
template force,  without  having  to  take  into  our  account 
the  resistance  or  rigidity  of  matter.  Two  statical  forces, 
thus  acting  at  a  mathematical  point,  are  equivalent,  in 
all  respects,  to  some  single  force  acting  at  the  same  point ; 
and  would  be  kept  in  equilibrium  by  a  force  equal  and 
opposite  to  that  single  force.  And  the  rule  by  which 
the  single  force  is  derived  from  the  two,  is  commonly 
termed  the  parallelogram  of  forces;  the  proposition  being 
this, — That  if  the  two  forces  be  represented  in  magnitude 
and  direction  by  the  two  sides  of  a  parallelogram,  the 
resulting  force  will  be  represented  in  the  same  manner 
by  the  diagonal  of  the  parallelogram.  This  proposition 
has  very  frequently  been  made,  by  modern  writers,  the 
commencement  of  the  science  of  Mechanics:  a  position 
for  which,  by  its  simplicity,  it  is  well  suited ;  although, 
in  order  to  deduce  from  it  the  other  elementary  proposi- 
tions of  the  science,  as,  for  instance,  those  respecting  the 
lever,  we  require  the  axiom  stated  in  the  last  section. 
9.  The  Parallelogram  of  Forces  is  a  necessary  Truth. 

In   the  series    of  discussions  in   which  we  are  here 

engaged,  our  main  business  is  to  ascertain  the  nature  and 
grounds  of  the  certainty  of  scientific  truths.  We  have, 
therefore,  to  ask  whether  this  proposition,  the  parallelo- 
gram of  forces,  be  a  necessary  truth ;  and  if  so,  on  what 
grounds  its  necessity  ultimately  rests.  We  shall  find 
that  this,  like  the  other  fundamental  doctrines  of  Statics, 
justly  claims  a  demonstrative  certainty.  Daniel  Ber- 
noulli, in  1726,  gave  the  first  proof  of  this  important 

o  2 


196          PHILOSOPHY  OF  THE  MECHANICAL  SCIENCES. 

proposition  on  pure  statical  principles ;  and  thus,  as  lie 
says*,  "  proved  that  statical  theorems  are  not  less 
necessarily  true  than  geometrical  are."  If  we  examine 
this  proof  of  Bernoulli,  in  order  to  discover  what  are  the 
principles  on  which  it  rests,  we  shall  find  that  the 
reasoning  employs  in  its  progress  such  axioms  as  this ; — 
That  if  from  forces  which  are  in  equilibrium  at  a  point 
be  taken  away  other  forces  which  are  in  equilibrium  at 
the  same  point,  the  remainder  will  be  in  equilibrium ; 
and  generally  ; — That  if  forces  can  be  resolved  into  other 
equivalent  forces,  these  may  be  separated,  grouped,  and 
recombined,  in  any  new  manner,  and  the  result  will  still 
be  identical  with  what  it  was  at  first.  Thus  in  Ber- 
noulli's proof,  the  two  forces  to  be  compounded  are  repre- 
sented by  P  and  Q;  P  is  resolved  into  two  other  forces,  x 
and  u ;  and  Q,  into  two  others,  Y  and  v,  under  certain 
conditions.  It  is  then  assumed  that  these  forces  may  be 
grouped  into  the  pairs  x,  Y,  and  u,  v :  and  when  it  has 
been  shown  that  x  and  Y  are  in  equilibrium,  they  may,  by 
what  has  been  said,  be  removed,  and  the  forces  P,  Q,  are 
equivalent  to  u,  v ;  which,  .being  in  the  same  direction  by 
the  course  of  the  construction,  have  a  result  equal  to 
their  sum. 

It  is  clear  that  the  principles  here  assumed  are 
genuine  axioms,  depending  upon  our  conception  of  the 
nature  of  equivalence  of  forces,  and  upon  their  being 
capable  of  addition  and  composition.  If  the  forces  P,  Q, 
be  equivalent  to  forces  x,  u,  Y,  v,  they  are  equivalent  to 
these  forces  added  and  compounded  in  any  order ;  just  as 
a  geometrical  figure  is,  by  our  conception  of  space, 
equivalent  to  its  parts  added  together  in  any  order.  The 
apprehension  of  forces  as  having  magnitude,  as  made 
up  of  parts,  as  capable  of  composition,  leads  to  such 
axioms  in  Statics,  in  the  same  manner  as  the  like 

*  Comm.  Petrop.  vol.  i. 


ESTABLISHMENT  OF  THE  PRINCIPLES  OF  STATICS.       197 

apprehension  of  space  leads  to  the  axioms  of  Geometry. 
And  thus  the  truths  of  Statics,  resting  upon  such  foun- 
dations, are  independent  of  experience  in  the  same 
manner  in  which  geometrical  truths  are  so. 

The  proof  of  the  parallelogram  of  forces  thus  given 
by  Daniel  Bernoulli,  as  it  was  the  first,  is  also  one  of 
the  most  simple  proofs  of  that  proposition  which  have 
been  devised  up  to  the  present  day.  Many  other 
demonstrations,  however,  have  been  given  of  the  same 
proposition.  Jacobi,  a  German  mathematician,  has  col- 
lected and  examined  eighteen  of  these*.  They  all  depend 
either  upon  such  principles  as  have  just  been  stated; 
That  forces  may  in  every  way  be  replaced  by  those  which 
are  equivalent  to  them ; — or  else  upon  those  previously 
stated,  the  doctrine  of  the  lever,  and  the  transfer  of  a 
force  from  one  point  to  another  of  its  direction.  In 
either  case,  they  are  necessary  results  of  our  statical 
conceptions,  independent  of  any  observed  laws  of  motion, 
and  indeed,  of  the  conception  of  actual  motion  altogether. 

There  is  another  class  of  alleged  proofs  of  the  paral- 
lelogram of  forces,  which  involve  the  consideration  of  the 
motion  produced  by  the  forces.  But  such  reasonings 
are,  in  fact,  altogether  irrelevant  to  the  subject  of  Statics. 
In  that  science,  forces  are  not  measured  by  the  motion 
which  they  produce,  but  by  the  forces  which  they  will 
balance,  as  we  have  already  seen.  The  combination  of 
two  forces  employed  in  producing  motion  in  the  same 
body,  either  simultaneously  or  successively,  belongs  to 
that  part  of  Mechanics  which  has  motion  for  its  subject, 
and  is  to  be  considered  in  treating  of  the  laws  of  motion. 
The  composition  of  motion,  (as  when  a  man  moves  in  a 

*  These  are  by  the  following  mathematicians;  D.  Bernoulli 
(1726);  Lambert  (1771) ;  Scarella  (1756) ;  Venini  (1764);  Araldi 
(1806);  Wachter  (1815);  Kaestner;  Marini;  Eytelwein;  Salimbeni; 
Duchayla;  two  different  proofs  by  Foncenex  (1760);  three  by 
D'Alembert ;  and  those  of  Laplace  and  M.  Poisson. 


198          PHILOSOPHY  OF  THE  MECHANICAL  SCIENCES. 

ship  while  the  ship  moves  through  the  water,)  has  con- 
stantly been  confounded  with  the  composition  of  force. 
But  though  this  has  been  done  by  very  eminent  mathe- 
maticians, it  is  quite  necessary  for  us  to  keep  the  two 
subjects  distinct,  in  order  to  see  the  real  nature  of  the 
evidence  of  truth  in  either  case.  The  conditions  of 
equilibrium  of  two  forces  on  a  lever,  or  of  three  forces  at 
a  point,  can  be  established  without  any  reference  what- 
ever to  any  motions  which  the  forces  might,  under  other 
circumstances,  produce.  And  because  this  can  be  done, 
to  do  so  is  the  only  scientific  procedure.  To  prove 
such  propositions  by  any  other  course,  would  be  to 
support  truth  by  extraneous  and  inconclusive  reasons ; 
which  would  be  foreign  to  our  purpose,  since  we  seek 
not  only  knowledge,  but  the  grounds  of  our  knowledge. 

1 0.  The  Centre  of  Gravity  seeks  the  lowest  place. — The 
principles  which  we  have  already  mentioned  afford  a 
sufficient  basis  for  the  science  of  Statics  in  its  most 
extensive  and  varied  applications ;  and  the  conditions  of 
equilibrium  of  the  most  complex  combinations  of  ma- 
chinery may  be  deduced  from  these  principles  with  a 
rigour  not  inferior  to  that  of  geometry.  But  in  some  of  the 
more  complex  cases,  the  results  of  long  trains  of  reasoning 
may  be  foreseen,  in  virtue  of  certain  maxims  which 
appear  to  us  self-evident,  although  it  may  not  be  easy  to 
trace  the  exact  dependence  of  these  maxims  upon  our  fun- 
damental conceptions  of  force  and  matter.  Of  this  nature 
is  the  maxim  now  stated ; — That  in  any  combination  of 
matter  any  how  supported,  the  Centre  of  Gravity  will 
descend  into  the  lowest  position  which  the  connexion  of 
the  parts  allows  it  to  assume  by  descending.  It  is  easily 
seen  that  this  maxim  carries  to  a  much  greater  extent 
the  principle  which  the  Greek  mathematicians  assumed, 
that  every  body  has  a  Centre  of  Gravity,  that  is,  a  point 
in  which,  if  the  whole  matter  of  the  body  be  collected, 


ESTABLISHMENT  OF  THE  PRINCIPLES  OF  STATICS.       199 

the  effect  will  remain  unchanged.  For  the  Greeks 
asserted  this  of  a  single  rigid  mass  only ;  whereas,  in  the 
maxim  now  under  our  notice,  it  is  asserted  of  any  masses, 
connected  by  strings,  rods,  joints,  or  in  any  manner. 
We  have  already  seen  that  more  modern  writers  on 
mechanics,  desirous  of  assuming  as  fundamental  no  wider 
principles  than  are  absolutely  necessary,  have  not  adopted 
the  Greek  axiom  in  all  its  generality,  but  have  only 
asserted  that  two  equal  weights  have  a  centre  of  gravity 
midway  between  them.  Yet  the  principle  that  every 
body,  however  irregular,  has  a  centre  of  gravity,  and  will 
be  supported  if  that  centre  is  supported,  and  not  otherwise, 
is  so  far  evident,  that  it  might  be  employed  as  a  funda- 
mental truth,  if  we  could  not  resolve  it  into  any  simpler 
truths :  and,  historically  speaking,  it  was  assumed  as 
evident  by  the  Greeks.  In  like  manner  the  still  wider 
principle,  that  a  collection  of  bodies,  as,  for  instance,  a 
flexible  chain  hanging  upon  one  or  more  supports,  has  a 
centre  of  gravity ;  and  that  this  point  will  descend  to  the 
lowest  possible  situation,  as  a  single  body  would  do,  has 
been  adopted  at  various  periods  in  the  history  of  mechan- 
ics; and  especially  at  conjunctures  when  mathematical 
philosophers  have  had  new  and  difficult  problems  to  con- 
tend with.  For  in  almost  every  instance  it  has  only 
been  by  repeated  struggles  that  philosophers  have  reduced 
the  solution  of  such  problems  to  a  clear  dependence  upon 
the  most  simple  axioms. 

11.  Stevinus's  Proof  for  Oblique  Forces. — We  have 
an  example  of  this  mode  of  dealing  with  problems,  in 
Stevinus's  mode  of  reasoning  concerning  the  Inclined 
Plane ;  which,  as  we  have  stated  in  the  History  of 
Mechanics,  was  the  first  correct  published  solution  of 
that  problem.  Stevinus  supposes  a  loop  of  chain,  or  a 
loop  of  string  loaded  with  a  series  of  equal  balls  at 
equal  distances,  to  hang  over  the  Inclined  Plane;  and 
his  reasoning  proceeds  upon  this  assumption, — That 


200  PHILOSOPHY  OF  THE  MECHANICAL  SCIENCES. 

such  a  loop  so  hanging  will  find  a  certain  position  in 
which  it  will  rest :  for  otherwise,  says  he  *,  its  motion 
must  go  on  for  ever,  which  is  absurd.  It  may  be  asked 
how  this  absurdity  of  a  perpetual  motion  appears ;  and  it 
will  perhaps  be  added,  that  although  the  impossibility  of 
a  machine  with  such  a  condition  may  be  proved  as  a 
remote  result  of  mechanical  principles,  this  impossibility 
can  hardly  be  itself  recognised  as  a  self-evident  truth. 
But  to  this  we  may  reply,  that  the  impossibility  is  really 
evident  in  the  case  contemplated  by  Stevinus;  for  we 
cannot  conceive  a  loop  of  chain  to  go  on  through  all 
eternity,  sliding  round  and  round  upon  its  support,  by  the 
effect  of  its  own  weight.  And  the  ground  of  our  convic- 
tion that  this  cannot  be,  seems  to  be  this  consideration ; 
that  when  the  chain  moves  by  the  effect  of  its  weight,  we 
consider  its  motion  as  the  result  of  an  effort  to  reach  some 
certain  position,  in  which  it  can  rest ;  just  as  a  single  ball 
in  a  bowl  moves  till  it  comes  to  rest  at  the  lowest  point 
of  the  bowl.  Such  an  effect  of  weight  in  the  chain,  we 
may  represent  to  ourselves  by  conceiving  all  the  matter 
of  the  chain  to  be  collected  in  one  single  point,  and  this 
single  heavy  point  to  hang  from  the  support  in  some  way 
or  other,  so  as  fitly  to  represent  the  mode  of  support  of 
the  chain.  In  whatever  manner  this  heavy  point  (the 
centre  of  gravity  of  the  chain)  be  supported  and  con- 
trolled in  its  movements,  there  will  still  be  some  position 
of  rest  which  it  will  seek  and  find.  And  thus  there  will 
be  some  corresponding  position  of  rest  for  the  chain ;  and 
the  interminable  shifting  from  one  position  to  another, 
with  no  disposition  to  rest  in  any  position,  cannot  exist. 

Thus  the  demonstration  of  the  property  of  the 
Inclined  Plane  by  Stevinus,  depends  upon  a  principle 
which,  though  far  from  being  the  simplest  of  those  to 
which  the  case  can  be  reduced,  is  still  both  true  and 
evident:  and  the  evidence  of  this  principle,  depending 
*  STEVIN.  Sfatique^  livre  i.,  prop.  19. 


ESTABLISHMENT  OF  THE  PRINCIPLES  OF  STATICS.      201 

upon  the  assumption  of  a  centre  of  gravity,  is  of  the  same 
nature  as  the  evidence  of  the  Greek  statical  demonstra- 
tions, the  earliest  real  advances  in  the  science. 

12.  Principle  of  Virtual  Velocities.  —  We  have 
referred  above  to  an  assertion  often  made,  that  we 
may,  from  the  simple  principles  of  Mechanics,  demon- 
strate the  impossibility  of  a  perpetual  motion.  In  reality, 
however,  the  simplest  proof  of  that  impossibility,  in 
a  machine  acted  upon  by  weight  only,  arises  from  the 
very  maxim  above  stated,  that  the  centre  of  gravity  seeks 
and  finds  the  lowest  place ;  or  from  some  similar  pro- 
position. For  if,  as  is  done  by  many  writers,  we  profess 
to  prove  the  impossibility  of  a  perpetual  motion  by  means 
of  that  proposition  which  includes  the  conditions  of  equi- 
librium, and  is  called  the  Principle  of  Virtual  Velocities*, 
we  are  under  the  necessity  of  first  proving  in  a  general 
manner  that  principle.  And  if  this  be  done  by  a  mere 
enumeration  of  cases,  (as  by  taking  those  five  cases  which 
are  called  the  mechanical  powers,)  there  may  remain  some 
doubts  whether  the  enumeration  of  possible  mechanical 
combinations  be  complete.  Accordingly,  some  writers 
have  attempted  independent  and  general  proofs  of  the 
Principle  of  Virtual  Velocities;  and  these  proofs  rest 
upon  assumptions  of  the  same  nature  as  that  now  under 
notice.  This  is,  for  example,  the  case  with  Lagrange's 
proof,  which  depends  upon  what  he  calls  the  Principle 
of  Pulleys.  For  this  principle  is, — That  a  weight  any  how 
supported,  as  by  a  string  passing  round  any  number  of 
pulleys  any  how  placed,  will  be  at  rest  then  only,  when 
it  cannot  get  lower  by  any  small  motion  of  the  pulleys. 
And  thus  the  maxim  that  a  weight  will  descend  if  it  can, 
is  assumed  as  the  basis  of  this  proof. 

There  is,  as  we  have  said,  no  need  to  assume  such 
principles  as  these  for  the  foundation  of  our  mechanical 
science.  But  it  is,  on  various  accounts,  useful  to  direct 
*  Sec  Hist.  Ind.  ScL,  \\.  41. 


202          PHILOSOPHY  OF  THE  MECHANICAL  SCIENCES. 

our  attention  to  those  cases  in  which  truths,  apprehended 
at  first  in  a  complex  and  derivative  form,  have  afterwards 
been  reduced  to  their  simpler  elements ;  in  which,  also, 
sagacious  and  inventive  men  have  fixed  upon  those 
truths  as  self-evident,  which  now  appear  to  us  only  cer- 
tain in  virtue  of  demonstration.  In  these  cases  we  can 
hardly  doubt  that  such  men  were  led  to  assert  the  doc- 
trines which  they  discovered,  not  by  any  capricious  con- 
jecture or  arbitrary  selection,  but  by  having  a  keener 
and  deeper  insight  than  other  persons  into  the  relations 
which  were  the  object  of  their  contemplation ;  and  in  the 
science  now  spoken  of,  they  were  led  to  their  assumptions 
by  possessing  clearly  and  distinctly  the  conceptions  of 
mechanical  cause  and  effect, — action  and  reaction, — force, 
and  the  nature  of  its  operation. 

13.  Fluids  press  Equally  in  all  Directions. — The  doc- 
trines which  concern  the  equilibrium  of  fluids  depend  on 
principles  no  less  certain  and  simple  than  those  which 
refer  to  the  equilibrium  of  solid  bodies ;  and  the  Greeks, 
who,  as  we  have  seen,  obtained  a  clear  view  of  some  of 
the  principles  of  Statics,  also  made  a  beginning  in  the 
kindred  subject  of  Hydrostatics.  We  still  possess  a  trea- 
tise of  Archimedes  On  Floating  Bodies,  which  contains 
correct  solutions  of  several  problems  belonging  to  this 
subject,  and  of  some  which  are  by  no  means  easy.  In 
this  treatise,  the  fundamental  assumption  is  of  this  kind : 
"  Let  it  be  assumed  that  the  nature  of  a  fluid  is  such, 
that  the  parts  which  are  less  pressed  yield  to  those  which 
are  more  pressed."  In  this  assumption  or  axiom  it  is 
implied  that  a  pressure  exerted  upon  a  fluid  in  one  direc- 
tion produces  a  pressure  in  another  direction ;  thus,  the 
weight  of  the  fluid  which  arises  from  a  downward  force 
produces  a  lateral  pressure  against  the  sides  of  the  con- 
taining vessel.  Not  only  does  the  pressure  thus  diverge 
from  its  original  direction  into  all  other  directions,  but  it 
is  in  all  directions  exactly  equal,  an  equal  extent  of  the 


ESTABLISHMENT  OF  THE  PRINCIPLES  OF  STATICS.      203 

fluid  being  taken.  This  principle,  which  was  involved  in 
the  reasoning  of  Archimedes,  is  still  to  the  present  day 
the  basis  of  all  hydrostatical  treatises,  and  is  expressed, 
as  above,  by  saying  that  fluids  press  equally  in  all  direc- 
tions. 

Concerning  this,  as  concerning  previously-noticed 
principles,  we  have  to  ask  whether  it  can  rightly  be  said 
to  be  derived  from  experience.  And  to  this  the  answer 
must  still  be,  as  in  the  former  cases,  that  the  proposition 
is  not  one  borrowed  from  experience  in  any  usual  or  exact 
sense  of  the  phrase.  I  will  endeavour  to  illustrate  this. 
There  are  many  elementary  propositions  in  physics,  our 
knowledge  of  which  indisputably  depends  upon  expe- 
rience ;  and  in  these  cases  there  is  no  difficulty  in  seeing 
the  evidence  of  this  dependence.  In  such  cases,  the  ex- 
periments which  prove  the  law  are  prominently  stated  in 
treatises  upon  the  subject :  they  are  given  with  exact 
measures,  and  with  an  account  of  the  means  by  which 
errors  were  avoided :  the  experiments  of  more  recent 
times  have  either  rendered  more  certain  the  law  ori- 
ginally asserted,  or  have  pointed  out  some  correction  of 
it  as  requisite  :  and  the  names,  both  of  the  discoverers  of 
the  law  and  of  its  subsequent  reformers,  are  well  known. 
For  instance,  the  proposition  that  "  The  elastic  force  of  air 
varies  as  the  density,"  was  first  proved  by  Boyle,  by  means 
of  operations  of  which  the  detail  is  given  in  his  Defence 
of  his  Pneumatical  Experiments* ;  and  by  Marriotte  in  his 
Traite  de  VEquilibre  des  Liquides,  from  whom  it  has  gene- 
rally been  termed  Marriotte's  law.  After  being  confirmed 
by  many  other  experimenters,  this  law  was  suspected  to 
be  slightly  inaccurate,  and  a  commission  of  the  French 
Academy  of  Sciences  was  appointed,  consisting  of  several 
distinguished  philosophers!,  to  ascertain  the  truth  or  false- 

*  SHAW'S  Boyle^  vol.  ii.,  p.  671. 

t  The  members  were  Prony,  Arago,  Ampere,  Girard,  and  Dulong. 


204          PHILOSOPHY  OF  THE  MECHANICAL  SCIENCES. 

hood  of  this  suspicion.  The  result  of  their  investigations 
appeared  to  be,  that  the  law  is  exact,  as  nearly  as  the 
inevitable  inaccuracies  of  machinery  and  measures  will 
allow  us  to  judge.  Here  we  have  an  example  of  a  law 
which  is  of  the  simplest  kind  and  form ;  and  which  yet  is 
not  allowed  to  rest  upon  its  simplicity  or  apparent  proba- 
bility, but  is  rigorously  tested  by  experience.  In  this 
case,  the  assertion,  that  the  law  depends  upon  experience, 
contains  a  reference  to  plain  and  notorious  passages  in  the 
history  of  science. 

Now  with  regard  to  the  principle  that  fluids  press 
equally  in  all  directions,  the  case  is  altogether  different. 
It  is,  indeed,  often  asserted  in  works  on  hydrostatics,  that 
the  principle  is  collected  from  experience,  and  sometimes 
a  few  experiments  are  described  as  exhibiting  its  effect ; 
but  these  are  such  as  to  illustrate  and  explain,  rather 
than  to  prove,  the  truth  of  the  principle:  they  are  never 
related  to  have  been  made  with  that  exactness  of  pre- 
caution and  measurement,  or  that  frequency  of  repetition, 
which  are  necessary  to  establish  a  purely  experimental 
truth.  Nor  did  such  experiments  occur  as  important 
steps  in  the  history  of  science.  It  does  not  appear  that 
Archimedes  thought  experiment  necessary  to  confirm  the 
truth  of  the  law  as  he  employed  it :  on  the  contrary,  he 
states  it  in  exactly  the  same  shape  as  the  axioms  which 
he  employs  in  statics,  and  even  in  geometry ;  namely,  as 
an  assumption.  Nor  does  any  intelligent  student  of  the 
subject  find  any  difficulty  in  assenting  to  this  fundamental 
principle  of  hydrostatics  as  soon  as  it  is  propounded  to 
him.  Experiment  was  not  requisite  for  its  discovery; 
experiment  is  not  necessary  for  its  proof  at  present ;  and 

The  experiments  were  extended  to  a  pressure  of  twenty-seven  atmo- 
spheres ;  and  in  no  instance  did  the  difference  between  the  observed 
and  calculated  elasticity  amount  to  one-hundredth  of  the  whole ;  nor 
did  the  difference  appear  to  increase  with  the  increase  of  pressure. — 
FECHNER.  Rcpcrtorium,  i.  110. 


ESTABLISHMENT  OF  THE  PRINCIPLES  OF  STATICS.      205 

we  may  add,  that  experiment,  though  it  may  make  the 
proposition  more  readily  intelligible,  can  add  nothing  to 
our  conviction  of  its  truth  when  it  is  once  understood. 

14.  Foundation  of  the  above  Axiom. — But  it  will 
naturally  be  asked,  What  then  is  the  ground  of  our 
conviction  of  this  doctrine  of  the  equal  pressure  of  a 
fluid  in  all  directions?  And  to  this  I  reply,  that  the 
reasons  of  this  conviction  are  involved  in  our  idea  of  a 
fluid,  which  is  considered  as  matter,  and  therefore  as 
capable  of  receiving,  resisting,  and  transmitting  force 
according  to  the  general  conception  of  matter ;  and  which 
is  also  considered  as  matter  which  has  its  parts  perfectly 
moveable  among  one  another.  For  it  follows  from  these 
suppositions,  that  if  the  fluid  be  confined,  a  pressure 
which  thrusts  in  one  side  of  the  containing  vessel,  may 
cause  any  other  side  to  bulge  outwards,  if  there  be  a  part 
of  the  surface  which  has  not  strength  to  resist  this  pressure 
from  within.  And  that  this  pressure  when  thus  trans- 
ferred into  a  direction  different  from  the  original  one,  is 
not  altered  in  intensity,  depends  upon  this  consideration ; 
that  any  difference  in  the  two  pressures  would  be  consi- 
dered as  a  defect  of  perfect  fluidity,  since  the  fluidity 
would  be  still  more  complete,  if  this  entire  and  undimi- 
nished  transmission  of  pressure  in  all  directions  were 
supposed.  If,  for  instance,  the  lateral  pressure  were  less 
than  the  vertical,  this  could  be  conceived  no  other  way 
than  as  indicating  some  rigidity  or  adhesion  of  the  parts 
of  the  fluid.  When  the  fluidity  is  perfect,  the  two  pres- 
sures which  act  in  the  two  different  parts  of  the  fluid 
exactly  balance  each  other :  they  are  the  action  and  the 
reaction,  and  must  hence  be  equal  by  the  same  necessity 
as  two  directly  opposite  forces  in  statics. 

But  it  may  be  urged,  that  even  if  we  grant  that  this 
conception  of  a  perfect  fluid,  as  a  body  which  has  its  parts 
perfectly  moveable  among  each  other,  leads  us  necessarily 


206  PHILOSOPHY  OF  THE  MECHANICAL  SCIENCES. 

to  the  principle  of  the  equality  of  hydrostatic  pressure  in 
all  directions,  still  this  conception  itself  is  obtained  from 
experience,  or  suggested  by  observation.  And  to  this  we 
may  reply,  that  the  conception  of  a  fluid,  as  contemplated 
in  mechanical  theory,  cannot  be  said  to  be  derived  from 
experience,  except  in  the  same  manner  as  the  conception 
of  a  solid  and  rigid  body  may  be  said  to  be  acquired  by 
experience.  For  if  we  imagine  a  vessel  full  of  small, 
smooth  spherical  balls,  such  a  collection  of  balls  would 
approach  to  the  nature  of  a  fluid,  in  having  its  parts 
moveable  among  each  other ;  and  would  approach  to  per- 
fect fluidity,  as  the  balls  became  smoother  and  smaller. 
And  such  a  collection  of  balls  would  also  possess  the  sta- 
tical properties  of  a  fluid  ;  for  it  would  transmit  pressure 
out  of  a  vertical  into  a  lateral  (or  any  other)  direction,  in 
the  same  manner  as  a  fluid  would  do.  And  thus  a  col- 
lection of  solid  bodies  has  the  same  property  which  a 
fluid  has ;  and  the  science  of  Hydrostatics  borrows  from 
experience  no  principles  beyond  those  which  are  involved 
in  the  science  of  Statics  respecting  solids.  And  since  in 
this  latter  portion  of  science,  as  we  have  already  seen, 
none  of  the  principles  depend  for  their  evidence  upon  any 
special  experience,  the  doctrines  of  Hydrostatics  also  are 
not  proved  by  experience,  but  have  a  necessary  truth 
borrowed  from  the  relations  of  our  ideas. 

It  is  hardly  to  be  expected  that  the  above  reasoning 
will,  at  first  sight,  produce  conviction  in  the  mind  of  the 
reader,  except  he  have,  to  a  certain  extent,  acquainted 
himself  with  the  elementary  doctrines  of  the  science  of 
Hydrostatics  as  usually  delivered ;  and  have  followed, 
with  clear  and  steady  apprehension,  some  of  the  trains  of 
reasoning  by  which  the  pressures  of  fluids  are  deter- 
mined ;  as,  for  instance,  the  explanation  of  what  is  called 
the  Hydrostatic  Paradox.  The  necessity  of  such  a  dis- 
cipline in  order  that  the  reader  may  enter  fully  into  this 


ESTABLISHMENT  OF  THE  PRINCIPLES  OF  STATICS.       207 

part  of  our  speculations,  naturally  renders  them  less 
popular ;  but  this  disadvantage  is  inevitable  in  our  plan. 
We  cannot  expect  to  throw  light  upon  philosophy  by 
means  of  the  advances  which  have  been  made  in  the 
mathematical  and  physical  sciences,  except  we  really 
understand  the  doctrines  which  have  been  firmly  esta- 
blished in  those  sciences.  This  preparation  for  philoso- 
phizing may  be  somewhat  laborious ;  but  such  labour  is 
necessary  if  we  would  pursue  speculative  truth  with  all 
the  advantages  which  the  present  condition  of  human 
knowledge  places  within  our  reach. 

We  may  add,  that  the  consequences  to  which  we  are 
directed  by  the  preceding  opinions,  are  of  very  great  im- 
portance in  their  bearing  upon  our  general  views  respect- 
ing human  knowledge.  I  trust  to  be  able  to  show,  that 
some  important  distinctions  are  illustrated,  some  perplex- 
ing paradoxes  solved,  and  some  large  anticipations  of  the 
future  extension  of  our  knowledge  suggested,  by  means  of 
the  conclusions  to  which  the  preceding  discussions  have 
conducted  us.  But  before  I  proceed  to  these  general 
topics,  I  must  consider  the  foundations  of  some  of  the 
remaining  portions  of  Mechanics. 


CHAPTER  VII. 

OF  THE  ESTABLISHMENT  OF  THE  PRINCIPLES 
OF  DYNAMICS. 

1.  IN  the  History  of  Mechanics,  I  have  traced  the 
steps  by  which  the  three  Laws  of  Motion  and  the  other 
principles  of  mechanics  were  discovered,  established,  and 
extended  to  the  widest  generality  of  form  and  applica- 
tion. We  have,  in  these  laws,  examples  of  principles 
which  were,  historically  speaking,  obtained  by  reference 
to  experience.  Bearing  in  mind  the  object  and  the  re- 
sult of  the  preceding  discussions,  we  cannot  but  turn 


203         PHILOSOPHY  OF  THE  MECHANICAL  SCIENCES. 

with  much  interest  to  examine  these  portions  of  science ; 
to  inquire  whether  there  be  any  real  difference  in  the 
grounds  and  nature  between  the  knowledge  thus  obtained, 
and  those  truths  which  we  have  already  contemplated  ; 
and  which,  as  we  have  seen,  contain  their  own  evidence, 
and  do  not  require  proof  from  experiment. 

2.  The  First  Law  of  Motion. — The  first  law  of  motion 
is,    that    When   a   body   moves   not   acted   upon   by   any 
force,   it   will  go   on  perpetually  in  a  straight   line,  and 
with  a  uniform  velocity.      Now  what  is  the  real  ground 
of  our  assent  to  this  proposition?     That  it  is  not  at  first 
sight  a  self-evident  truth,  appears  to  be  clear ;  since  from 
the  time  of  Aristotle  to  that  of  Galileo  the  opposite 
assertion  was  held  to  be  true;  and  it  was  believed  that 
all  bodies  in  motion  had,  by  their  own  nature,  a  constant 
tendency  to  move  more  and  more  slowly,  so  as  to  stop  at 
last.     This  belief,  indeed,  is  probably  even  now  enter- 
tained by  most  persons,  till  their  attention  is  fixed  upon 
the  arguments  by  which  the  first  law  of  motion  is  esta- 
blished.     It  is,  however,  not  difficult  to  lead  any  person 
of  a  speculative  habit  of  thought  to  see  that  the  retarda- 
tion which  constantly  takes  place  in  the  motion  of  all 
bodies  when  left  to  themselves,  is,  in  reality,  the  effect  of 
extraneous  forces   which  destroy   the   velocity.     A  top 
ceases  to  spin  because  the  friction  against  the  ground  and 
the  resistance  of  the  air  gradually  diminish  its  motion, 
and  not  because  its  motion  has  any  internal  principle  of 
decay  or  fatigue.     This  may  be  shown,  and  was,  in  fact, 
shown  by  Hooke  before  the  Royal  Society,  at  the  time 
when  the  laws  of  motion  were  still  under  discussion,  by 
means  of  experiments  in  which  the  weight  of  the  top  is 
increased,  and  the  resistance  to  motion  offered  by  its  sup- 
port, is  diminished ;  for  by  such  contrivances  its  motion  is 
made  to  continue  much  longer  than  it  would  otherwise 
do.     And  by  experiments  of  this  nature,  although  we  can 
never  remove  the  whole  of  the  external  impediments  to 


ESTABLISHMENT  OF  THE  PRINCIPLES  OF  DYNAMICS.       209 

continued  motion,  and  although,  consequently,  there  will 
always  be  some  retardation  ;  and  an  end  of  the  motion  of 
a  body  left  to  itself,  however  long  it  may  be  delayed,  must 
at  last  come ;  yet  we  can  establish  a  conviction  that  if  all 
resistance  could  be  removed,  there  would  be  no  diminution 
of  velocity,  and  thus  the  motion  would  go  on  for  ever. 

If  we  call  to  mind  the  axioms  which  we  formerly  stated, 
as  containing  the  most  important  conditions  involved  in 
the  idea  of  Cause,  it  will  be  seen  that  our  conviction 
in  this  case  depends  upon  the  first  axiom  of  Causation, 
that  nothing  can  happen  without  a  cause.  Every  change 
in  the  velocity  of  the  moving  body  must  have  a  cause ; 
and  if  the  change  can,  in  any  manner,  be  referred  to  the 
presence  of  other  bodies,  these  are  said  to  exert  force  upon 
the  moving  body:  and  the  conception  of  force  is  thus 
evolved  from  the  general  idea  of  cause.  Force  is  any 
cause  which  has  motion,  or  change  of  motion,  for  its  effect ; 
and  thus,  all  the  change  of  velocity  of  a  body  which  can 
be  referred  to  extraneous  bodies,  as  the  air  which  sur- 
rounds it,  or  the  support  on  which  it  rests,  is  considered 
as  the  effect  of  forces ;  and  this  consideration  looked 
upon  as  explaining  the  difference  between  the  motion 
which  really  takes  place  in  the  experiment,  and  that 
which,  as  the  law  asserts,  would  take  place  if  the  body 
were  not  acted  on  by  any  forces. 

Thus  the  truth  of  the  first  law  of  motion  depends 
upon  the  axiom  that  no  change  can  take  place  without  a 
cause ;  and  follows  from  the  definition  of  force,  if  we  sup- 
pose that  there  can  be  none  but  an  external  cause  of  change. 
But  in  order  to  establish  the  law,  it  was  necessary  further 
to  be  assured  that  there  is  no  internal  cause  of  change  of 
velocity  belonging  to  all  matter  whatever,  and  operating 
in  such  a  manner  that  the  mere  progress  of  time  is  suffi- 
cient to  produce  a  diminution  of  velocity  in  all  moving 
bodies.  It  appears  from  the  history  of  mechanical  science, 

VOL.  i.  p 


210          PHILOSOPHY  OF  THE  MECHANICAL  SCIENCES. 

that  this  latter  step  required  a  reference  to  observation 
and  experiment ;  and  that  the  first  law  of  motion  is  so 
far,  historically  at  least,  dependent  upon  our  experience. 

But  notwithstanding  this  historical  evidence  of  the 
need  which  we  have  of  a  reference  to  observed  facts,  in 
order  to  place  this  first  law  of  motion  out  of  doubt,  it  has 
been  maintained  by  very  eminent  mathematicians  and 
philosophers,  that  the  law  is,  in  truth,  evident  of  itself, 
and  does  not  really  rest  upon  experimental  proof.  Such, 
for  example,  is  the  opinion  of  D'Alembert*,  who  offers 
what  is  called  an  a  priori  proof  of  this  law ;  that  is,  a 
demonstration  derived  from  our  ideas  alone.  When  a 
body  is  put  in  motion,  either,  he  says,  the  cause  which 
puts  it  in  motion  at  first,  suffices  to  make  it  move  one 
foot,  or  the  continued  action  of  the  cause  during  this  foot 
is  requisite  for  the  motion.  In  the  first  case,  the  same 
reason  which  made  the  body  proceed  to  the  end  of  the  first 
foot  will  hold  for  its  going  on  through  a  second,  a  third, 
a  fourth  foot,  and  so  on  for  any  number.  In  the  second 
case,  the  same  reason  which  made  the  force  continue  to  act 
during  the  first  foot,  will  hold  for  its  acting,  and  therefore 
for  the  body  moving  during  each  succeeding  foot.  And 
thus  the  body,  once  beginning  to  move,  must  go  on 
moving  for  ever. 

It  is  obvious  that  we  might  reply  to  this  argument, 
that  the  reasons  for  the  body  proceeding  during  each 
succeeding  foot  may  not  necessarily  be  all  the  same  ;  for 
among  these  reasons  may  be  the  time  which  has  elapsed  ; 
and  thus  the  velocity  may  undergo  a  change  as  the  time 
proceeds :  and  we  require  observation  to  inform  us  that 
it  does  not  do  so. 

Professor  Playfair  has  presented  nearly  the  same  argu- 
ment, although  in  a  different  and  more  mathematical 
formf.  If  the  velocity  change,  says  he,  it  must  change 

*  Dynamique.  t  Outlines,  £c.5  p.  26. 


ESTABLISHMENT  OP  THE  PRINCIPLES  OF  DYNAMICS.      211 

according  to  some  expression  of  calculation  depending 
upon  the  time,  or,  in  mathematical  language,  must  be  a 
function  of  the  time.  If  the  velocity  diminish  as  the 
time  increases,  this  may  be  expressed  by  stating  the 
velocity  in  each  case  as  a  certain  number,  from  which 
another  quantity,  or  term,  increasing  as  the  time  increases, 
is  subtracted.  But,  Playfair  adds,  there  is  no  condition 
involved  in  the  nature  of  the  case,  by  which  the  coefficients, 
or  numbers  which  are  to  be  employed,  along  with  the 
number  representing  the  time,  in  calculating  this  second 
term,  can  be  determined  to  be  of  one  magnitude  rather 
than  of  any  other.  Therefore  he  infers  there  can  be  no 
such  coefficients,  and  that  the  velocity  is  in  each  case  equal 
to  some  constant  number,  independent  of  the  time ;  and 
is  therefore  the  same  for  all  times. 

In  reply  to  this  we  may  observe,  that  the  circum- 
stance of  our  not  seeing  in  the  nature  of  the  case  any- 
thing which  determines  for  us  the  coefficients  above 
spoken  off,  cannot  prove  that  they  have  not  some  certain 
value  in  nature.  We  do  not  see  in  the  nature  of  the 
case  anything  which  should  determine  a  body  to  fall  six- 
teen feet  in  a  second  of  time,  rather  than  one  foot  or  one 
hundred  feet :  yet  in  fact  the  space  thus  run  through  by 
falling  bodies  is  determined  to  a  certain  magnitude.  It 
would  be  easy  to  assign  a  mathematical  expression  for 
the  velocity  of  a  body,  implying  that  one-hundredth  of 
the  velocity,  or  any  other  fraction,  is  lost  in  each  second*: 
and  where  is  the  absurdity  of  supposing  such  an  expres- 
sion really  to  represent  the  velocity? 

Most  modern  writers  on  mechanics  have  embraced 
the  opposite  opinion,  and  have  ascribed  our  knowledge  of 

*  This  would  be  the  case,  if,  t  being  the  number  of  seconds 
elapsed,  and  C  some  constant  quantity,  the  velocity  were  expressed  by 
this  mathematical  formula, 

C  f — 

i  —  .  p  2 


212          PHILOSOPHY  OF  THE  MECHANICAL  SCIENCES. 

this  first  law  of  motion  to  experience.  Thus  M.  Poisson, 
one  of  the  most  eminent  of  the  mathematicians  who  have 
written  on  this  subject,  says*,  "We  cannot  affirm  a 
priori  that  the  velocity  communicated  to  a  body  will  not 
become  slower  and  slower  of  itself,  and  end  by  being 
entirely  extinguished.  It  is  only  by  experience  and 
induction  that  this  question  can  be  decided." 

Yet  it  cannot  be  denied  that  there  is  much  force  in 
those  arguments  by  which  it  is  attempted  to  shew  that 
the  First  Law  of  Motion,  such  as  we  find  it,  is  more  con- 
sonant to  our  conceptions  than  any  other  would  be.  The 
Law,  as  it  exists,  is  the  most  simple  that  we  can  conceive. 
Instead  of  having  to  determine  by  experiments  what  is 
the  law  of  the  natural  change  of  velocity,  we  find  the  Law 
to  be  that  it  does  not  change  at  all.  To  a  certain 
extent,  the  Law  depends  upon  the  evident  axiom,  that  no 
change  can  take  place  without  a  cause.  But  the  ques- 
tion further  occurs,  whether  the  mere  lapse  of  time  may 
not  be  a  cause  of  change  of  velocity.  In  order  to  ensure 
this,  we  have  recourse  to  experiment ;  and  the  result  is 
that  time  alone  does  not  produce  any  such  change.  In 
addition  to  the  conditions  of  change  which  we  collect 
from  our  own  ideas,  we  ask  of  experience  what  other 
conditions  and  circumstances  she  has  to  offer ;  and  the 
answer  is,  that  she  can  point  out  none.  When  we  have 
removed  the  alterations  which  external  causes,  in  our 
very  conception  of  them,  occasion,  there  are  no  longer 
any  alterations.  Instead  of  having  to  guide  ourselves  by 
experience,  we  learn  that  on  this  subject  she  has  nothing 
to  tell  us.  Instead  of  having  to  take  into  account  a  num- 
ber of  circumstances,  we  find  that  we  have  only  to 
reject  all  circumstances.  The  velocity  of  a  body  remains 
unaltered  by  time  alone,  of  whatever  kind  the  body 
itself  be. 

But  the  doctrine  that  time  alone  is  not  a  cause  of 

*  POISSON.  Dynamique.  Ed.  2,  Art.  113. 


ESTABLISHMENT  OF  THE  PRINCIPLES  OF  DYNAMICS.      213 

change  of  velocity  in  any  body  is  further  recommended 
to  us  by  this  consideration ; — that  time  is  conceived  by 
us  not  as  a  cause,  but  only  as  a  condition  of  other  causes 
producing1  their  effects.  Causes  operate  in  time ;  but  it 
is  only  when  the  cause  exists  that  the  lapse  of  time  can 
give  rise  to  alterations.  When  therefore  all  external 
causes  of  change  of  velocity  are  supposed  to  be  removed, 
the  velocity  must  continue  identical  with  itself,  whatever 
the  time  which  elapses.  An  eternity  of  negation  can 
produce  no  positive  result. 

Thus,  though  the  discovery  of  the  First  Law  of 
Motion  was  made,  historically  speaking,  by  means  of 
experiment,  we  have  now  attained  a  point  of  view  in 
which  we  see  that  it  might  have  been  certainly  known 
to  be  true  independently  of  experience.  This  law  in  its 
ultimate  form,  when  completely  simplified  and  steadily 
contemplated,  assumes  the  character  of  a  self-evident 
truth.  We  shall  find  the  same  process  to  take  place  in 
other  instances.  And  this  feature  in  the  progress  of 
science  will  hereafter  be  found  to  suggest  very  important 
views  with  regard  both  to  the  nature  and  prospects  of  our 
knowledge. 

2.  Gravity  is  a  Uniform  Force. — We  shall  find 
observations  of  the  same  kind  offering  themselves  in  a 
manner  more  or  less  obvious,  with  regard  to  the  other 
principles  of  Dynamics.  The  determination  of  the  laws 
according  to  which  bodies  fall  downwards  by  the  common 
action  of  gravity,  has  already  been  noticed  in  the  History 
of  Mechanics*,  as  one  of  the  earliest  positive  advances 
in  the  doctrine  of  motion.  These  laws  were  first  rightly 
stated  by  Galileo,  and  established  by  reasoning  and  by 
experiment,  not  without  dissent  and  controversy.  The 
amount  of  these  doctrines  is  this :  That  gravity  is  a 
uniform  accelerating  force  ;  such  a  uniform  force  having 
this  for  its  character,  that  it  makes  the  velocity  increase  in 

*  Hist.  Tnd.  Sci.y  ii.  26. 


214         PHILOSOPHY  OF  THE  MECHANICAL  SCIENCES. 

exact  proportion  to  the  time  of  motion.  The  relation  which 
the  spaces  described  by  the  body  bear  to  the  times  in 
which  they  are  described,  is  obtained  by  mathematical 
deduction  from  this  definition  of  the  force. 

The  clear  Definition  of  a  uniform  accelerating  force, 
and  the  Proposition  that  gravity  is  such  a  force,  were 
co-ordinate  and  contemporary  steps  in  this  discovery. 
In  defining  accelerating  force,  reference,  tacit  or  ex- 
press, was  necessarily  made  to  the  second  of  the  general 
axioms  respecting  causation, — That  causes  are  measured 
by  their  effects.  Force,  in  the  cases  now  under  our 
notice,  is  conceived  to  be,  as  we  have  already  stated, 
(p.  209,)  any  cause  which,  acting  from  without,  changes 
the  motion  of  a  body.  It  must,  therefore,  in  this  accep- 
tation, be  measured  by  the  magnitude  of  the  changes 
which  are  produced.  But  in  what  manner  the  changes 
of  motion  are  to  be  employed  as  the  measures  of  force,  is 
learnt  from  observation  of  the  facts  which  we  see  taking- 
place  in  the  world.  Experience  interprets  the  axiom  of 
causation,  from  which  otherwise  we  could  not  deduce 
any  real  knowledge.  We  may  assume,  in  virtue  of  our 
general  conceptions  of  force,  that  under  the  same  circum- 
stances, a  greater  change  of  motion  implies  a  greater  force 
producing  it ;  but  what  are  we  to  expect  when  the  cir- 
cumstances change?  The  weight  of  a  body  makes  it 
fall  from  rest  at  first,  and  causes  it  to  move  more  quickly 
as  it  descends  lower.  We  may  express  this  by  saying, 
that  gravity,  the  universal  force  which  makes  all  terres- 
trial bodies  fall  when  not  supported,  by  its  continuous 
action  first  gives  velocity  to  the  body  when  it  has  none, 
and  afterwards  adds  velocity  to  that  which  the  body 
already  has.  But  how  is  the  velocity  added  proportioned 
to  the  velocity  which  already  exists?  Force  acting  on  a 
body  at  rest,  and  on  a  body  in  motion,  appears  under 
very  different  conditions ; — how  are  the  effects  related  ? 
Let  the  force  be  conceived  to  be  in  both  cases  the 


ESTABLISHMENT  OF  THE  PRINCIPLES  OF  DYNAMICS.      215 

same,  since  force  is  conceived  to  depend  upon  the  extra- 
neous bodies,  and  not  upon  the  condition  of  the  moving 
mass  itself.  But  the  force  being  the  same,  the  effects 
may  still  be  different.  It  is  at  first  sight  conceivable 
that  the  body,"  acted  upon  by  the  same  gravity,  may 
receive  a  less  addition  of  velocity  when  it  is  already 
moving  in  the  direction  in  which  this  gravity  impels  it ; 
for  if  we  ourselves  push  a  body  forwards,  we  can  produce 
little  additional  effect  upon  it  when  it  is  already  moving 
rapidly  away  from  us.  May  it  not  be  true,  in  like  man- 
ner, that  although  gravity  be  always  the  same  force,  its 
effect  depends  upon  the  velocity  which  the  body  under 
its  influence  already  possesses? 

Observation  and  reasoning  combined,  as  we  have 
said,  enabled  Galileo  to  answer  these  questions.  He 
asserted  and  proved  that  we  may  consistently  and  properly 
measure  a  force  by  the  velocity  which  is  by  it  generated 
in  a  body,  in  some  certain  time,  as  one  second;  and 
further,  that  if  we  adopt  this  measure,  gravity  will  be  a 
force  of  the  same  value  under  all  circumstances  of  the 
body  which  it  affects ;  since  it  appeared  that,  in  fact,  a 
falling  body  does  receive  equal  increments  of  velocity 
in  equal  times  from  first  to  last. 

If  it  be  asked  whether  we  could  have  known,  anterior 
to,  or  independent  of,  experiment,  that  gravity  is  a 
uniform  force  in  the  sense  thus  imposed  upon  the  term ; 
it  appears  clear  that  we  must  reply  5  that  we  could  not 
have  attained  to  such  knowledge,  since  other  laws  of  the 
motion  of  bodies  downwards  are  easily  conceivable,  and 
nothing  but  observation  could  inform  us  that  one  of 
these  laws  does  not  prevail  in  fact.  Indeed,  we  may  add, 
that  the  assertion  that  the  force  of  gravity  is  uniform,  is 
so  far  from  being  self-evident,  that  it  is  not  even  true ; 
for  gravity  varies  according  to  the  distance  from  the 
centre  of  the  earth ;  and  although  this  variation  is  so 


216  PHILOSOPHY  OF  THE  MECHANICAL  SCIENCES. 

small  as  to  be,  in  the  case  of  falling  bodies,  imperceptible, 
it  negatives  the  rigorous  uniformity  of  the  force  as  com- 
pletely, though  not  to  the  same  extent,  as  if  the  weight 
of  a  body  diminished  in  a  marked  degree,  when  it  was 
carried  from  the  lower  to  the  upper  room  of  a  house.  It 
cannot,  then,  be  a  truth  independent  of  experience,  that 
gravity  is  uniform. 

Yet,  in  fact,  the  assertion  that  gravity  is  uniform  was 
assented  to,  not  only  before  it  was  proved,  but  even 
before  it  was  clearly  understood.  It  was  readily  granted 
by  all,  that  bodies  which  fall  freely  are  uniformly  accele- 
rated ;  but  while  some  held  the  opinion  just  stated,  that 
uniformly  accelerated  motion  is  that  in  which  the  velocity 
increases  in  proportion  to  the  time,  others  maintained, 
that  that  is  uniformly  accelerated  motion,  in  which  the 
velocity  increases  in  proportion  to  the  space ;  so  that,  for 
example,  a  body  in  falling  vertically  through  twenty  feet 
should  acquire  twice  as  great  a  velocity  as  one  which 
falls  through  ten  feet. 

These  two  opinions  are  both  put  forward  by  the 
interlocutors  of  Galileo's  dialogue  on  this  subject*. 
And  the  latter  supposition  is  rejected,  the  author  showing, 
not  that  it  is  inconsistent  with  experience,  but  that  it  is 
impossible  in  itself:  inasmuch  as  it  would  inevitably  lead 
to  the  conclusion,  that  the  fall  though  a  large  and  a 
small  vertical  space  would  occupy  exactly  the  same  time. 
Indeed,  Galileo  assumes  his  definition  of  uniformly 
accelerated  motion  as  one  which  is  sufficiently  recom- 
mended by  its  own  simplicity.  "  If  we  attend  carefully," 
he  says,  "  we  shall  find  that  no  mode  of  increase  of  velocity 
is  more  simple  than  that  which  adds  equal  increments  in 
equal  times.  Which  we  may  easily  understand  if  we 
consider  the  close  affinity  of  time  and  motion :  for  as  the 
uniformity  of  motion  is  defined  by  the  equality  of  spaces 
*  Dlalogo,  iii.  p.  95,  t  Ibid.  p.  91. 


ESTABLISHMENT  OF  THE  PRINCIPLES  OF  DYNAMICS.      217 

described  in  equal  times,  so  we  may  conceive  the  uni- 
formity of  acceleration  to  exist  when  equal  velocities  are 
added  in  equal  times." 

Galileo's  mode  of  supporting  his  opinion,  that  bodies 
falling  by  the  action  of  gravity  are  thus  uniformly  acce- 
lerated, consists,  in  the  first  place,  in  adducing  the 
maxim  that  nature  always  employs  the  most  simple 
means *.  But  he  is  far  from  considering  this  a  decisive 
argument.  "  I,"  says  one  of  his  speakers,  "  as  it  would 
be  very  unreasonable  in  me  to  gainsay  this  or  any  other 
definition  which  any  author  may  please  to  make,  since 
they  are  all  arbitrary,  may  still,  without  offence,  doubt 
whether  such  a  definition,  conceived  and  admitted  in  the 
abstract,  fits,  agrees,  and  is  verified  in  that  kind  of 
accelerated  motion  which  bodies  have  when  they  descend 
naturally." 

The  experimental  proof  that  bodies,  when  they  fall 
downwards,  are  uniformly  accelerated,  is  (by  Galileo) 
derived  from  the  inclined  plane ;  and  therefore  assumes 
the  proposition,  that  if  such  uniform  acceleration  prevail 
in  vertical  motion,  it  will  also  hold  when  a  body  is  com- 
pelled to  describe  an  oblique  rectilinear  path.  This  pro- 
position may  be  shown  to  be  true,  if  (assuming  by  anti- 
cipation the  Third  Law  of  Motion,  of  which  we  shall 
shortly  have  to  speak,)  we  introduce  the  conception  of 
a  uniform  statical  force  as  the  cause  of  uniform  acce- 
leration. For  the  force  on  the  inclined  plane  bears 
a  constant  proportion  to  the  vertical  force,  and  this 
proportion  is  known  from  statical  considerations.  But 
in  the  work  of  which  we  are  speaking,  Galileo  does 
not  introduce  this  abstract  conception  of  force  as  the 
foundation  of  his  doctrines.  Instead  of  this,  he  pro- 
poses, as  a  postulate  sufficiently  evident  to  be  made 
the  basis  of  his  reasonings,  That  bodies  which  descend 

*   Dialogo,  iii.  p.  91. 


218          PHILOSOPHY  OF  THE  MECHANICAL  SCIENCES. 

clown  inclined  planes  of  different  inclinations,  but  of 
the  same  vertical  height,  all  acquire  the  same  velocity*. 
But  when  this  postulate  has  been  propounded  by  one 
of  the  persons  of  the  dialogue,  another  interlocutor  says, 
"  You  discourse  very  probably ;  but  besides  this  like- 
lihood, I  wish  to  augment  the  probability  so  far,  that 
it  shall  be  almost  as  complete  as  a  necessary  demon- 
stration." He  then  proceeds  to  describe  a  very  inge- 
nious and  simple  experiment,  which  shows  that  when  a 
body  is  made  to  swing  upwards  at  the  end  of  a  string, 
it  attains  to  the  same  height,  whatever  is  the  path  it 
follows,  so  long  as  it  starts  from  the  lowest  point  with 
the  same  velocity.  And  thus  Galileo's  postulate  is  ex- 
perimentally confirmed,  so  far  as  the  force  of  gravity  can 
be  taken  as  an  example  of  the  forces  which  the  postulate 
contemplates  :  and  conversely,  gravity  is  proved  to  be  a 
uniform  force,  so  far  as  it  can  be  considered  clear  that 
the  postulate  is  true  of  uniform  forces. 

When  we  have  introduced  the  conception  and  defi- 
nition of  accelerating  force,  Galileo's  postulate,  that 
bodies  descending  down  inclined  planes  of  the  same 
vertical  height,  acquire  the  same  velocity,  may,  by  a 
few  steps  of  reasoning,  be  demonstrated  to  be  true  of 
uniform  forces  :  and  thus  the  proof  that  gravity,  either  in 
vertical  or  oblique  motion,  is  a  uniform  force,  is  confirmed 
by  the  experiment  above  mentioned ;  as  it  also  is,  on 
like  grounds,  by  many  other  experiments,  made  upon 
inclined  planes  and  pendulums. 

Thus  the  propriety  of  Galileo's  conception  of  a  uni- 
form force,  and  the  doctrine  that  gravity  is  a  uniform 
force,  were  confirmed  by  the  same  reasonings  and  experi- 
ments. We  may  make  here  two  remarks  ;  First,  that  the 
conception,  when  established  and  rightly  stated,  appears 
so  simple  as  hardly  to  require  experimental  proof;  a 
remark  which  we  have  already  made  with  regard  to  the 

)  iii.  p.  36. 


ESTABLISHMENT  OF  THE  PRINCIPLES  OF  DYNAMICS.        219 

First  Law  of  Motion :  and  Second,  that  the  discovery  of 
the  real  law  of  nature  was  made  by  assuming  propositions 
which,  without  further  proof,  we  should  consider  as  very 
precarious,  and  as  far  less  obvious,  as  well  as  less  evident, 
than  the  law  of  nature  in  its  simple  form. 

3.  The  Second  Law  of  Motion. — When  a  body,  instead 
of  falling  downwards  from  rest,  is  thrown  in  any  direc- 
tion, it  describes  a  curve  line,  till  its  motion  is  stopped. 
In  this,  and  in  all  other  cases  in  which  a  body  describes 
a  curved  path  in  free  space,  its  motion  is  determined  by 
the  Second  Law  of  Motion.  The  law,  in  its  general 
form,  is  as  follows: — When  a  body  is  thus  cast  forth 
and  acted  upon  by  a  force  in  a  direction  transverse  to  its 
motion,  the  result  is,  That  there  is  combined  with  the 
motion  with  which  the  body  is  throivn,  another  motion, 
exactly  the  same  as  that  which  the  same  force  would  have 
communicated  to  a  body  at  rest. 

It  will  readily  be  understood  that  the  basis  of  this 
law  is  the  axiom  already  stated,  that  effects  are  measured 
by  their  causes.  In  virtue  of  this  axiom,  the  effect  of 
gravity  acting  upon  a  body  in  a  direction  transverse  to  its 
motion,  must  measure  the  accelerative  or  deflective  force 
of  gravity  under  those  circumstances.  If  this  effect  vary 
with  the  varying  velocity  and  direction  of  the  body  thus 
acted  upon,  the  deflective  force  of  gravity  also  will  vary 
with  those  circumstances.  The  more  simple  supposition 
is,  that  the  deflective  force  of  gravity  is  the  same,  whatever 
be  the  velocity  and  direction  of  the  body  which  is  sub- 
jected to  its  influence :  and  this  is  the  supposition  which 
we  find  to  be  verified  by  facts.  For  example,  a  ball  let 
fall  from  the  top  of  a  ship's  upright  mast,  when  she  is 
sailing  steadily  forward,  will  fall  at  the  foot  of  the  mast, 
just  as  if  it  were  let  fall  while  the  ship  were  at  rest ;  thus 
showing  that  the  motion  which  gravity  gives  to  the  ball 
is  compounded  with  the  horizontal  motion  which  the  ball 


220          PHILOSOPHY  OF  THE  MECHANICAL  SCIENCES. 

shares  with  the  ship  from  the  first.  This  general  and 
simple  conception  of  motions  as  compounded  with  one 
another,  represents,  it  is  proved,  the  manner  in  which  the 
motion  produced  by  gravity  modifies  any  other  motion 
which  the  body  may  previously  have  had. 

The  discussions  which  terminated  in  the  general 
reception  of  this  Second  Law  of  Motion  among  mechani- 
cal writers,  were  much  mixed  up  with  the  arguments  for 
and  against  the  Copernican  system,  which  system  repre- 
sented the  earth  as  revolving  upon  its  axis.  For  the 
obvious  argument  against  this  system  was,  that  if  the 
earth  were  thus  in  motion  from  west  to  east,  a  stone 
dropt  from  the  top  of  a  tower  would  be  left  behind,  the 
tower  moving  away  from  it :  and  the  answer  was,  that  by 
this  law  of  motion,  the  stone  would  have  the  earth's 
motion  impressed  upon  it,  as  well  as  that  motion  which 
would  arise  from  its  gravity  to  the  earth ;  and  that  the 
motion  of  the  stone  relative  to  the  tower  would  thus  be 
the  same  as  if  both  earth  and  tower  were  at  rest.  Gali- 
leo further  urged,  as  a  presumption  in  favour  of  the 
opinion  that  the  two  motions, — the  circular  motion  arising 
from  the  rotation  of  the  earth,  and  the  downward  motion 
arising  from  the  gravity  of  the  stone,  would  be  com- 
pounded in  the  way  we  have  described,  (neither  of  them 
disturbing  or  diminishing  the  other,)  —  that  the  first 
motion  was  in  its  own  nature  not  liable  to  any  change  or 
diminution*,  as  we  learn  from  the  First  Law  of  Motion. 
Nor  was  the  subject  lightly  dismissed.  The  experiment 
of  the  stone  let  fall  from  the  top  of  the  mast  was  made 
in  various  forms  by  Gassendi;  and  in  his  Epistle,  De 
Motu  impwsso  a  Motore  translate,  the  rule  now  in  question 
is  supported  by  reference  to  these  experiments.  In  this 
manner,  the  general  truth,  the  Second  Law  of  Motion, 
was  established  completely  and  beyond  dispute. 

*  Dialogo,  ii.  p.  114. 


ESTABLISHMENT  OF  THE  PRINCIPLES  OF  DYNAMICS.      221. 

But  when  this  law  had  been  proved  to  be  true  in  a 
general  sense,  with  such  accuracy  as  rude  experiments, 
like  those  of  Galileo  and  Gassendi,  would  admit,  it  still 
remained  to  be  ascertained  (supposing  our  knowledge  of 
the  law  to  be  the  result  of  experience  alone,)  whether  it 
were  true  with  that  precise  and  rigorous  exactness  which 
more  refined  modes  of  experimenting  could  test.  We 
so  willingly  believe  in  the  simplicity  of  laws  of  nature, 
that  the  rigorous  accuracy  of  such  a  law,  known  to  be  at 
least  approximately  true,  was  taken  for  granted,  till  some 
ground  for  suspecting  the  contrary  should  appear.  Yet 
calculations  have  not  been  wanting  which  might  confirm 
the  law  as  true  to  the  last  degree  of  accuracy.  Laplace 
relates  (Syst.  du  Monde,  livre  iv.,  chap.  16,)  that  at  one 
time  he  had  conceived  it  possible  that  the  effect  of  gravity 
upon  the  moon  might  be  slightly  modified  by  the  moon's 
direction  and  velocity ;  and  that  in  this  way  an  explana- 
tion might  be  found  for  the  moon's  acceleration  (a  devia- 
tion of  her  observed  from  her  calculated  place,  which  long 
perplexed  mathematicians).  But  it  was  after  some  time 
discovered  that  this  feature  in  the  moon's  motion  arose 
from  another  cause ;  and  the  second  law  of  motion  was 
confirmed  as  true  in  the  most  rigorous  sense. 

Thus  we  see  that  although  there  were  arguments 
which  might  be  urged  in  favour  of  this  law,  founded 
upon  the  necessary  relations  of  ideas,  men  became  con- 
vinced of  its  truth  only  when  it  was  verified  and  con- 
firmed by  actual  experiment.  But  yet  in  this  case 
again,  as  in  the  former  ones,  when  the  law  had  been 
established  beyond  doubt  or  question,  men  were  very 
ready  to  believe  that  it  was  not  a  mere  result  of  observa- 
tion,— that  the  truth  which  it  contained  was  not  derived 
from  experience, — that  it  might  have  been  assumed  as 
true  in  virtue  of  reasonings  anterior  to  experience, — and 
that  experiments  served  only  to  make  the  law  more  plain 


222          PHILOSOPHY  OF  THE  MECHANICAL  SCIENCES. 

and  intelligible,  as  visible  diagrams  in  geometry  serve  to 
illustrate  geometrical  truths ;  our  knowledge  not  being 
(they  deemed)  in  mechanics,  any  more  than  in  geometry, 
borrowed  from  the  senses.  It  was  thought  by  many  to  be 
self-evident,  that  the  effect  of  a  force  in  any  direction 
cannot  be  increased  or  diminished  by  any  motion  trans- 
verse to  the  direction  of  the  force  which  the  body  may 
have  at  the  same  time :  or,  to  express  it  otherwise,  that 
if  the  motion  of  the  body  be  compounded  of  a  horizontal 
and  vertical  motion,  the  vertical  motion  alone  will  be 
affected  by  the  vertical  force.  This  principle,  indeed,  not 
only  has  appeared  evident  to  many  persons,  but  even  at  the 
present  day  is  assumed  as  an  axiom  by  many  of  the  most 
eminent  mathematicians.  It  is,  for  example,  so  employed 
in  the  Mecanique  Celeste  of  Laplace,  which  may  be  looked 
upon  as  the  standard  of  mathematical  mechanics  in  our 
time  ;  and  in  the  Mecanique  Analytique  of  Lagrange,  the 
most  consummate  example  which  has  appeared  of  sub- 
tilty  of  thought  on  such  subjects,  as  well  as  of  power  of 
mathematical  generalization*.  And  thus  we  have  here 

*  I  may  observe  that  the  rule  that  we  may  compound  motions,  as 
the  Law  supposes,  is  involved  in  the  step  of  resolving  them ;  which  is 
done  in  the  passage  to  which  I  refer  (Mec.  Analyt.  ptie.  i.,  sect,  i.,  art. 
3,  p.  225).  "  Si  on  concoit  que  la  mouvement  d'un  corps  et  les  forces 
qui  le  sollicitent  soient  decomposes  suivant  trois  lignes  droites  perpen- 
diculaires  entre  elles,  on  pourra  considerer  separement  les  mouvemens 
et  les  forces  relatives  a  chacun  a  de  ces  trois  directions.  Car  a  cause  de 
la  perpendicularite  des  directions  il  est  visible  que  chacun  de  ces  mouve- 
mens partiels  peut  etre  regarde  comme  independant  des  deux  autres, 
et  qu'il  ne  peut  recevoir  d'alteration  que  de  la  part  de  la  force  qui  agit 
dans  la  direction  de  ce  mouvement ;  Ton  peut  conclure  que  ces  trois 
mouvements  doivent  suivre,  chacun  en  particulier,  les  lois  des  mouve- 
mens rectilignes  acceleres  ou  retardes  par  les  forces  donnees."  Laplace 
makes  the  same  assumption  in  effect,  (Mec.  Cel.  p.  i ,  liv.  i.,  art.  7>) 
by  resolving  the  forces  which  act  upon  a  point  in  three  rectangular 
directions,  and  reasoning  separately  concerning  each  direction.  But  in 
his  mode  of  treating  the  subject  is  involved  a  principle  which  belongs 
to  the  Third  Law  of  Motion,  namely,  the  doctrine  that  the  velocity  is 
as  the  force,  of  which  we  shall  have  to  speak  elsewhere. 


ESTABLISHMENT  OF  THE  PRINCIPLES  OF  DYNAMICS.      223 

another  example  of  that  circumstance  which  we  have 
already  noticed  in  speaking  of  the  First  Law  of  Motion, 
(p.  213,)  and  of  the  Law  that  Gravity  is  a  uniform  Force, 
(p.  218) ;  namely,  that  the  law,  though  historically  esta- 
blished by  experiments,  appears,  when  once  discovered 
and  reduced  to  its  most  simple  and  general  form,  to  be 
self-evident.  I  am  the  more  desirous  of  drawing  atten- 
tion to  this  feature  in  various  portions  of  the  history  of 
science,  inasmuch  as  it  will  be  found  to  lead  to  some  very 
extensive  and  important  views,  hereafter  to  be  con- 
sidered. 

4.  The  Third  Law  of  Motion. — We  have,  in  the 
definition  of  Accelerating  Force,  a  measure  of  Forces,  so 
far  as  they  are  concerned  in  producing  motion.  We  had 
before,  in  speaking  of  the  principles  of  statics,  defined 
the  measure  of  Forces  or  Pressures,  so  far  as  they  are 
employed  in  producing  equilibrium.  But  these  two 
aspects  of  Force  are  closely  connected ;  and  we  require  a 
law  which  shall  lay  down  the  rule  of  their  connexion. 
By  the  same  kind  of  muscular  exertion  by  which  we  can 
support  a  heavy  stone,  we  can  also  put  it  in  motion.  The 
question  then  occurs,  how  is  the  rate  and  manner  of  its 
motion  determined  ?  The  answer  to  this  question  is  con- 
tained in  the  Third  Law  of  Motion,  and  it  is  to  this  effect : 
that  the  Momentum  which  any  pressure  produces  in  the 
mass  in  a  given  time  is  proportional  to  the  pressure.  By 
momentum  is  meant  the  product  of  the  numbers  which 
express  the  velocity  and  the  mass  of  the  body :  and  hence, 
if  the  mass  of  the  body  be  the  same  in  the  instances 
which  we  compare,  the  rule  is, — That  the  velocity  is  as  the 
force  which  produces  it ;  and  this  is  one  of  the  simplest 
ways  of  expressing  the  Third  Law  of  Motion. 

In  agreement  with  our  general  plan,  we  have  to  ask, 
What  is  the  ground  of  this  rule  ?  What  is  the  simplest 
and  most  satisfactory  form  to  which  we  can  reduce  the 


224          PHILOSOPHY  OF  THE  MECHANICAL  SCIENCES. 

proof  of  it?  Or,  to  take  an  instance  ;  if  a  double  pres- 
sure be  exerted  against  a  given  mass,  so  disposed  as  to 
be  capable  of  motion,  why  must  it  produce  twice  the 
velocity  in  the  same  time  ? 

To  answer  this  question,  suppose  the  double  pressure 
to  be  resolved  into  two  single  pressures :  one  of  these 
will  produce  a  certain  velocity ;  and  the  question  is,  why 
an  equal  pressure,  acting  upon  the  same  mass,  will  pro- 
duce an  equal  velocity^  addition  to  the  former?  Or, 
stating  the  matter  otherwise,  the  question  is,  why  each 
of  the  two  forces  will  produce  its  separate  effect,  unal- 
tered by  the  simultaneous  action  of  the  other  force  ? 

This  statement  of  the  case  makes  it  seem  to  approach 
very  near  to  such  cases  as  are  included  in  the  Second  Law 
of  Motion,  and  therefore  it  might  appear  that  this  Third 
Law  has  no  grounds  distinct  from  the  Second.  But  it  must 
be  recollected  that  the  workforce  has  a  different  meaning 
in  this  case  and  in  that ;  in  this  place  it  signifies  pressure ; 
in  the  statement  of  the  Second  Law  its  import  was  acce- 
lerative  or  deflective  force,  measured  by  the  velocity  or 
deflexion  generated.  And  thus  the  Third  Law  of  Motion? 
so  far  as  our  reasonings  yet  go,  appears  to  rest  on  a 
foundation  different  from  the  Second. 

Accordingly,  that  part  of  the  Third  Law  of  Motion 
which  we  are  now  considering,  that  the  velocity  generated 
is  as  the  force,  was  obtained,  in  fact,  by  a  separate  train 
of  research.  The  first  exemplification  of  this  law  which 
was  studied  by  mathematicians,  was  the  motion  of  bodies 
upon  inclined  planes :  for  the  force  which  urges  a  body 
clown  an  inclined  plane  is  known  by  statics,  and  hence 
the  velocity  of  its  descent  was  to  be  determined.  Galileo 
originally*  in  his  attempts  to  solve  this  problem  of  the 
descent  of  a  body  down  an  inclined  plane,  did  not  proceed 

*  Dial,  della  Sc.  Nuov.  Hi.,  p.  96.  See  Hist.  Ind.  Sci.y  ii., 
p.  47. 


ESTABLISHMENT  OF  THE  PRINCIPLES  OF  DYNAMICS.       225 

from  the  principle  which  we  have  stated,  (the  determina- 
tion of  the  force  which  acts  down  the  inclined  plane  from 
statical  considerations,)  obvious  as  it  may  seem ;  but 
assumed,  as  we  have  already  seen,  a  proposition  appa- 
rently far  more  precarious  ; — namely,  that  a  body  sliding 
down  a  smooth  inclined  plane  acquires  always  the  same 
velocity,  so  long  as  the  vertical  height  fallen  through  is 
the  same.  And  this  conjecture,  (for  at  first  it  was  nothing 
more  than  a  conjecture,)  he  confirmed  by  an  ingenious 
experiment ;  in  which  bodies  acquired  or  lost  the  same 
velocity  by  descending  or  ascending  through  the  same 
height,  although  their  paths  were  different  in  other 
respects. 

This  was  the  form  in  which  the  doctrine  of  the  motion 
of  bodies  down  inclined  planes  was  at  first  presented  in 
Galileo's  Dialogues  on  the  Science  of  Motion.  But  his 
disciple  Viviani  was  dissatisfied  with  the  assumption  thus 
introduced  ;  and  in  succeeding  editions  of  the  Dialogues, 
the  apparent  chasm  in  the  reasoning  was  much  narrowed, 
by  making  the  proof  depend  upon  a  principle  nearly 
identical  with  the  third  law  of  motion  as  we  have  just 
stated  it.  In  the  proof  thus  added,  "  We  are  agreed," 
says  the  interlocutor*,  "that  in  a  moving  body  the 
impetus,  energy,  momentum,  or  propension  to  motion,  is 
as  great  as  is  the  force  or  least  resistance  which  suffices 
to  sustain  it ;"  and  the  impetus  or  momentum,  in  the 
course  of  the  proof,  being  taken  to  be  as  the  velocity 
produced  in  a  given  time,  it  is  manifest  that  the  principle 
so  stated  amounts  to  this ;  that  the  velocity  produced 
is  as  the  statical  force.  And  thus  this  law  of  motion 
appears,  in  the  school  of  Galileo,  to  have  been  suggested 
and  established  at  first  by  experiment,  but  afterwards 
confirmed  and  demonstrated  by  a  priori  considerations. 

We  see,  in  the  above  reasoning,  a  number  of  abstract 

*  Dialogo,  p.  104. 
VOL.  I.  Q 


226  PHILOSOPHY  OF  THE  MECHANICAL  SCIENCES. 

terms  introduced  which  are  not,  at  first  at  least,  very 
distinctly  defined,  as  impetus,  momentum,  &c.  Of 
these,  momentum  has  been  selected,  to  express  that 
quantity  which,  in  a  moving-  body,  measures  the  statical 
force  impressed  upon  the  body.  This  quantity  is,  as  we 
have  just  seen,  proportional  to  the  velocity  in  a  given 
body.  It  is  also,  in  different  bodies,  proportional  to  the 
mass  of  the  body.  This- part  of  the  third  law  of  motion 
follows  from  our  conception  of  matter  in  general  as  con- 
sisting of  parts  capable  of  addition.  A  double  pressure 
must  be  required  to  produce  the  same  velocity  in  a  double 
mass ;  for  if  the  mass  be  halved,  each  half  will  require 
an  equal  pressure ;  and  the  addition,  both  of  the  pres- 
sures and  of  the  masses,  will  take  place  without  disturb- 
ing the  effects. 

The  measure  of  the  quantity  of  matter  of  a  body  con- 
sidered as  affecting  the  velocity  which  pressure  produces 
in  the  body,  is  termed  its  inertia,  as  we  have  already 
stated,  (p.  182.)  Inertia  is  the  property  by  which  a 
large  mass  of  matter  requires  a  greater  force  than  a 
small  mass,  to  give  it  an  equal  velocity.  It  belongs  to 
each  portion  of  matter;  and  portions  of  inertia  are 
added  whenever  portions  of  matter  are  added.  Hence 
inertia  is  as  the  quantity  of  matter ;  which  is  only  ano- 
ther way  of  expressing  this  third  law  of  motion,  so  far 
as  quantity  of  matter  is  concerned. 

But  how  do  we  know  the  quantity  of  matter  of  a 
body  ?  We  may  reply,  that  we  take  the  weight  as  the 
measure  of  the  quantity  of  matter :  but  we  may  then  be 
again  asked,  how  it  appears  that  the  weight  is  propor- 
tional to  the  inertia ;  which  it  must  be,  in  order  that  the 
quantity  of  matter  may  be  proportional  to  both  one  and 
the  other.  We  answer,  that  this  appears  to  be  true 
experimentally,  because  all  bodies  fall  with  equal  veloci- 
ties by  gravity,  when  the  known  causes  of  difference  are 


ESTABLISHMENT  OF  THE  PRINCIPLES  OF  DYNAMICS.       227 

removed.  The  observations  of  falling  bodies,  indeed,  are 
not  susceptible  of  much  exactness :  but  experiments  lead- 
ing to  the  same  result,  and  capable  of  great  precision, 
were  made  upon  pendulums  by  Newton ;  as  he  relates  in 
The  Principia,  book  iii.,  prop.  6.  They  all  agreed,  he 
says,  with  perfect  accuracy :  and  thus  the  weight  and  the 
inertia  are  proportional  in  all  cases,  and  therefore  each 
proportional  to  the  quantity  of  matter  as  measured  by 
the  other. 

The  conception  of  inertia,  as  we  have  already  seen  in 
Chapter  V.,  involves  the  notion  of  action  and  reaction ; 
and  thus  the  laws  which  involve  inertia  depend  upon  the 
idea  of  mutual  causation.  The  rule,  that  the  velocity  is 
as  the  force,  depends  upon  the  principle  of  causation, 
that  the  effect  is  proportional  to  the  cause ;  the  effect 
being  here  so  estimated  as  to  be  consistent  both  with  the 
other  laws  of  motion  and  with  experiment. 

But  here,  as  in  other  cases,  the  question  occurs  again ; 
Is  experiment  really  requisite  for  the  proof  of  this  law? 
If  we  look  to  authorities,  we  shall  be  not  a  little  embar- 
rassed to  decide.  D'Alembert  is  against  the  necessity  of 
experimental  proof.  "Why,"  says  he*,  "should  we  have 
recourse  to  this  principle  employed,  at  the  present  day, 
by  everybody,  that  the  force  is  proportional  to  the  velo- 
city ?  .  .  .  a  principle  resting  solely  upon  this  vague  and 
obscure  axiom,  that  the  effect  is  proportional  to  the  cause. 
We  shall  not  examine  here,"  he  adds,  "  if  this  principle 
is  necessarily  true ;  we  shall  only  avow  that  the  proofs 
which  have  hitherto  been  adduced  do  not  appear  to  us 
unexceptionable:  nor  shall  we,  with  some  geometers, 
adopt  it  as  a  purely  contingent  truth ;  which  would  be 
to  ruin  the  certainty  of  mechanics,  and  to  reduce  it  to  be 
nothing  more  than  an  experimental  science.  We  shall 
content  ourselves  with  observing,"  he  proceeds,  "  that 

*  Dynamique,  Pref.  p.  x. 

Q  2 


228          PHILOSOPHY  OF  THE  MECHANICAL  SCIENCES. 

certain  or  doubtful,  clear  or  obscure,  it  is  useless  in  mecha- 
nics, and  consequently  ought  to  be  banished  from  the 
science."  Though  D'Alembert  rejects  the  third  law  of 
motion  in  this  form,  he  accepts  one  of  equivalent  import, 
which  appears  to  him  to  possess  axiomatic  certainty;  and 
this  procedure  is  in  consistence  with  the  course  which  he 
takes,  of  claiming  for  the  science  of  mechanics  more  than 
mere  experimental  truth.  On  the  contrary,  Laplace  con- 
siders this  third  law  as  established  by  experiment.  "  Is 
the  force,"  he  says*,  "proportional  to  the  velocity? 
This,"  he  replies,  "  we  cannot  know  a  priori,  seeing  that 
we  are  in  ignorance  of  the  nature  of  moving  force :  we 
must  therefore,  for  this  purpose,  recur  to  experience ;  for 
all  which  is  not  a  necessary  consequence  of  the  few  data 
we  have  respecting  the  nature  of  things,  is,  for  us,  only 
'a  result  of  observation."  And  again  he  saysf,  "Here, 
then,  we  have  two  laws  of  motion, — the  law  of  inertia  [the 
first  law  of  motion],  and  the  law  of  the  force  proportional 
to  the  velocity, — which  are  given  by  observation.  They 
are  the  most  natural  and  the  most  simple  laws  which  we 
can  imagine,  and  without  doubt  they  flow  from  the  very 
nature  of  matter ;  but  this  nature  being  unknown,  they 
are,  for  us,  only  observed  facts :  the  only  ones,  however, 
which  mechanics  borrows  from  experience." 

It  will  appear,  I  think,  from  the  views  given  in  this 
and  several  other  parts  of  the  present  work,  that  we  can- 
not with  justice  say  that  we  have  very  "  few  data  respect- 
ing the  nature  of  things,"  in  speculating  concerning  the 
laws  of  the  universe ;  since  all  the  consequences  which 
flow  from  the  relations  of  our  fundamental  ideas,  neces- 
sarily regulate  our  knowledge  of  things,  so  far  as  we  have 
any  such  knowledge.  Nor  can  we  say  that  the  nature  of 
matter  is  unknown  to  us,  in  any  sense  in  which  we  can 
conceive  knowledge  as  possible.  The  nature  of  matter  is 

*  Mec.  Cel.  p.  15.  t  P.  18. 


ESTABLISHMENT  OF  THE  PRINCIPLES  OF  DYNAMICS.      229 

no  more  unknown  than  the  nature  of  space  or  of  number. 
In  our  conception  of  matter,  as  of  space  and  of  number, 
are  involved  certain  relations,  which  are  the  necessary 
groundwork  of  our  knowledge ;  and  anything  which  is 
independent  of  these  relations,  is  not  unknown,  but 
inconceivable. 

It  must  be  already  clear  to  the  reader,  from  the 
phraseology  employed  by  these  two  eminent  mathema- 
ticians, that  the  question  respecting  the  formation  of  the 
third  law  of  motion  can  only  be  solved  by  a  careful  con- 
sideration of  what  we  mean  by  observation  and  experi- 
ence, nature  and  matter.  But  it  will  probably  be  gene- 
rally allowed,  that,  taking  into  account  the  explanations 
already  offered  of  the  necessary  conditions  of  experience 
and  of  the  conception  of  inertia,  this  law  of  motion,  that 
the  inertia  is  as  the  quantity  of  matter,  is  almost  or  alto- 
gether self-evident. 

5.  Action  and  Reaction  are  Equal  in  Moving  Bodies. 
— When  we  have  to  consider  bodies  as  acting  upon  one 
another,  and  influencing  each  other's  motions,  the  third 
law  of  motion  is  still  applied ;  but  along  with  this,  we 
also  employ  the  general  principle  that  action  and  reaction 
are  equal  and  opposite.  Action  and  reaction  are  here  to 
be  understood  as  momentum  produced  and  destroyed, 
according  to  the  measure  of  action  established  by  the 
third  law  of  motion :  and  the  cases  in  which  this  prin- 
ciple is  thus  employed  form  so  large  a  portion  of  those  in 
which  the  third  law  of  motion  is  used,  that  some  writers 
(Newton  at  the  head  of  them)  have  stated  the  equality  of 
action  and  reaction  as  the  third  law  of  motion. 

The  third  law  of  motion  being  once  established,  the 
equality  of  action  and  reaction,  in  the  sense  of  momentum 
gained  and  lost,  necessarily  follows.  Thus,  if  a  weight 
hanging  by  a  string  over  the  edge  of  a  smooth  level  table 
draw  another  weight  along  the  table,  the  hanging  weight 


230  PHILOSOPHY  OF  THE  MECHANICAL  SCIENCES. 

moves  more  slowly  than  it  would  do  if  not  so  connected, 
and  thus  loses  velocity  by  the  connexion ;  while  the  other 
.weight  gains  by  the  connexion  all  the  velocity  which  it 
has,  for  if  left  to  itself  it  would  rest.  And  the  pressures 
which  restrain  the  descent  of  the  first  body  and  accelerate 
that  of  the  second,  are  equal  at  all  instants  of  time,  for 
each  of  these  pressures  is  the  tension  of  the  string :  and 
hence,  by  the  third  law  of  motion,  the  momentum  gained 
by  the  one  body,  and  the  momentum  lost  by  the  other  in 
virtue  of  the  action  of  this  string,  are  equal.  And  similar 
reasoning  may  be  employed  in  any  other  case  where  bodies 
are  connected. 

The  case  where  one  body  does  not  push  or  draw,  but 
strikes  another,  appeared  at  first  to  mechanical  reasoners 
to  be  of  a  different  nature  from  the  others ;  but  a  little 
consideration  was  sufficient  to  show  that  a  blow  is,  in 
fact,  only  a  short  and  violent  pressure ;  and  that,  there- 
fore, the  general  rule  of  the  equality  of  momentum  lost 
and  gained  applies  to  this  as  well  as  to  the  other  cases. 

Thus,  in  order  to  determine  the  case  of  the  direct 
action  of  bodies  upon  one  another,  we  require  no  new  law 
of  motion.  The  equality  of  action  and  reaction,  which 
enters  necessarily  into  every  conception  of  mechanical 
operation,  combined  with  the  measure  of  action  as  given 
by  the  third  law  of  motion,  enables  us  to  trace  the  con- 
sequences of  every  case,  whether  of  pressure  or  of 
impact. 

6.  DAlemberfs  Principle. — But  what  will  be  the 
result  when  bodies  do  not  act  directly  upon  each  other, 
but  are  indirectly  connected  in  any  way  by  levers,  strings, 
pulleys,  or  in  any  other  manner,  so  that  one  part  of  the 
system  has  a  mechanical  advantage  over  another  ?  The 
result  must  still  be  determined  by  the  principle  that 
action  and  reaction  balance  each  other.  The  action  and 
reaction,  being  pressures  in  one  sense,  must  balance  each 


ESTABLISHMENT  OF  THE  PRINCIPLES  OF  DYNAMICS.      231 

other  by  the  laws  of  statics,  for  these  laws  determine 
the  equilibrium  of  pressure.  Now  action  and  reaction, 
according  to  their  measures  in  the  Third  Law  of  Motion, 
are  momentum  gained  and  lost,  when  the  action  is  direct; 
and  except  the  indirect  action  introduce  some  modifica- 
tion of  the  law,  they  must  have  the  same  measure  still. 
But,  in  fact,  we  cannot  well  conceive  any  modification  of 
the  law  to  take  place  in  this  case ;  for  direct  action  is  only 
one  (the  ultimate)  case  of  indirect  action.  Thus  if  two  heavy 
bodies  act  at  different  points  of  a  lever,  the  action  of  each 
on  the  other  is -indirect ;  but  if  the  two  points  come  toge- 
ther, the  action  becomes  direct.  Hence  the  rule  must  be 
that  which  we  have  already  stated ;  for  if  the  rule  were 
false  for  indirect  action,  it  would  also  be  false  for  direct 
action,  for  which  case  we  have  shown  it  to  be  true.  And 
thus  we  obtain  the  general  principle,  that  in  any  system 
of  bodies  which  act  on  each  other,  action  and  reaction, 
estimated  by  momentum  gained  and  lost,  balance  each 
other  according  to  the  laws  of  equilibrium.  This  prin- 
ciple, which  is  so  general  as  to  supply  a  key  to  the  solu- 
tion of  all  possible  mechanical  problems,  is  commonly 
called  D'Akmberts  Principle.  The  experimental  proofs 
which  convinced  men  of  the  truth  of  the  third  law  of 
motion  were,  many  or  most  of  them,  proofs  of  the  law  in 
this  extended  sense.  And  thus  the  proof  of  D'Alembert's 
Principle,  both  from  the  idea  of  mechanical  action  and 
from  experience,  is  included  in  the  proof  of  the  law 
already  stated. 

7.  Connexion  of  Dynamical  and  Statical  Principles — 
The  principle  of  equilibrium  of  D'Alembert  just  stated, 
is  the  law  which  he  would  substitute  for  the  third  law  of 
motion ;  and  he  would  thus  remove  the  necessity  for  an 
independent  proof  of  that  law.  In  like  mariner,  the 
second  law  of  motion  is  by  some  writers  derived  from  the 
principle  of  the  composition  of  statical  forces;  and  they 


232  PHILOSOPHY  OF  THE  MECHANICAL  SCIENCES. 

would  thus  supersede  the  necessity  of  a  reference  to 
experiment  in  that  case.  Laplace  takes  this  course,  and 
thus,  as  we  have  seen,  rests  only  the  first  and  third  law 
of  motion  upon  experience.  Newton,  on  the  other  hand, 
recognises  the  same  connexion  of  propositions,  but  for  a 
different  purpose ;  for  he  derives  the  composition  of 
statical  forces  from  the  second  law  of  motion. 

The  close  connexion  of  these  three  principles,  the 
composition  of  (statical)  forces,  the  composition  of  (acce- 
lerating) forces  with  velocities,  and  the  measure  of 
(moving)  forces  by  velocities,  cannot  be  denied ;  yet  it 
appears  to  be  by  no  means  easy  to  supersede  the  neces- 
sity of  independent  proofs  of  the  two  last  of  these  prin- 
ciples. Both  may  be  proved  or  illustrated  by  expe- 
riment: and  the  experiments  which  prove  the  one  are 
different  from  those  which  establish  the  other.  For 
example,  it  appears  by  easy  calculations,  that  when  we 
apply  our  principles  to  the  oscillations  of  a  pendulum, 
the  second  law  is  proved  by  the  fact,  that  the  oscillations 
take  place  at  the  same  rate  in  an  east  and  west,  and  in  a 
north  and  south  direction :  under  the  same  circumstances, 
the  third  law  is  proved  by  our  finding  that  the  time  of  a 
small  oscillation  is  proportional  to  the  square  root  of  the 
length  of  a  pendulum ;  and  similar  differences  might  be 
pointed  out  in  other  experiments,  as  to  their  bearing 
upon  the  one  law  or  the  other. 

8.  Mechanical  Principles  become  gradually  more 
simple  and  more  evident.- — I  will  again  point  out  in 
general  two  circumstances  which  I  have  already  noticed 
in  particular  cases  of  the  laws  of  motion.  Truths  are 
often  at  first  assumed  in  a  form  which  is  far  from  being 
the  most  obvious  or  simple ;  and  truths  once  discovered 
are  gradually  simplified,  so  as  to  assume  the  appearance 
of  self-evident  truths. 

The  former  circumstance  is  exemplified  in  several  of 


ESTABLISHMENT  OF  THE  PRINCIPLES  OF  DYNAMICS.       233 

the  instances  which  \ve  have  had  to  consider.  The 
assumption  that  a  perpetual  motion  is  impossible  pre- 
ceded the  knowledge  of  the  first  law  of  motion.  The 
assumed  equality  of  the  velocities  acquired  down  two 
inclined  planes  of  the  same  height,  was  afterwards  reduced 
to  the  third  law  of  motion  by  Galileo  himself.  In  the 
History*,  we  have  noted  Huyghens's  assumption  of  the 
equality  of  the  actual  descent  and  potential  ascent  of  the 
centre  of  gravity :  this  was  afterwards  reduced  by  Her- 
man and  the  Bernoulli s,  to  the  statical  equivalence  of  the 
solicitations  of  gravity  and  the  vicarious  solicitations  of 
the  effective  forces  which  act  on  each  point ;  and  finally 
to  the  principle  of  D'Alembert,  which  asserts  that  the 
motions  gained  and  lost  balance  each  other. 

This  assertion  of  principles  which  now  appear  neither 
obvious  nor  self-evident,  is  not  to  be  considered  as  a 
groundless  assertion  on  the  part  of  the  discoverers  by 
whom  it  was  made.  On  the  contrary,  it  is  evidence  of 
the  deep  sagacity  and  clear  thought  which  were  requisite 
in  order  to  make  such  discoveries.  For  these  results  are 
really  rigorous  consequences  of  the  laws  of  motion  in 
their  simplest  form :  and  the  evidence  of  them  was  pro- 
bably present,  though  undeveloped,  in  the  minds  of  the 
discoverers.  We  are  told  of  geometrical  students,  who, 
by  a  peculiar  aptitude  of  mind,  perceived  the  evidence  of 
some  of  the  more  advanced  "propositions  of  geometry 
without  going  through  the  introductory  steps.  We  must 
suppose  a  similar  aptitude  for  mechanical  reasonings, 
which  led  Stevinus,  Galileo,  Newton,  and  Huyghens,  to 
make  those  assumptions  which  finally  resolved  themselves 
into  the  laws  of  motion. 

We  may  observe  further,  that  the  simplicity  and  evi- 
dence which  the  laws  of  mechanics  have  at  length 
assumed,  are  much  favoured  by  the  usage  of  words  among 

*  Vol.  ii.  p.  82. 


234          PHILOSOPHY  OF  THE  MECHANICAL  SCIENCES. 

the  best  writers  on  such  subjects.  Terms  which  origi- 
nally, and  before  the  laws  of  motion  were  fully  known, 
were  used  in  a  very  vague  and  fluctuating  sense,  were 
afterwards  limited  and  rendered  precise,  so  that  assertions 
which  at  first  appear  identical  propositions  become  dis- 
tinct and  important  principles.  Thus  force,  motion, 
momentum,  are  terms  which  were  employed,  though  in  a 
loose  manner,  from  the  very  outset  of  mechanical  specu- 
lation. And  so  long  as  these  words  retained  the  vagueness 
of  common  language,  it  would  have  been  a  useless  and 
barren  truism  to  say  that  "  the  momentum  is  proportional 
to  the  force,"  or  that  "  a  body  loses  as  much  motion  as 
it  communicates  to  another."  But  when  "  momentum  " 
and  "  quantity  of  motion  "  are  defined  to  mean  the  pro- 
duct of  mass  and  velocity,  these  two  propositions  imme- 
diately become  distinct  statements  of  the  third  law  of 
motion  and  its  consequences.  In  like  manner,  the  asser- 
tion that  "  gravity  is  a  uniform  force "  was  assented  to, 
before  it  was  settled  what  a  uniform  force  was ;  but  this 
assertion  only  became  significant  and.  useful  when  that 
point  had  been  properly  determined.  The  statement 
that  "  when  different  motions  are  communicated  to  the 
same  body  their  effects  are  compounded,"  becomes  the 
second  law  of  motion,  when  we  define  what  composition 
of  motions  is.  And  the  same  process  may  be  observed 
in  other  cases. 

And  thus  we  see  how  well  the  form  which  science 
ultimately  assumes  is  adapted  to  simplify  it.  The  defi- 
nitions which  are  adopted,  and  the  terms  which  become 
current  in  precise  senses,  produce  a  complete  harmony 
between  the  matter  and  the  form  of  our  knowledge ;  so 
that  truths  which  were  at  first  unexpected  and  recondite, 
became  familiar  phrases,  and  after  a  few  generations 
sound,  even  to  common  ears,  like  identical  propositions. 

9.  Controversy  of  the  Measure  of  Force. — In  the  His- 


ESTABLISHMENT  OF  THE  PRINCIPLES  OF  DYNAMICS.      235 

tory  of  Mechanics*,  we  have  given  an  account  of  the 
controversy  which,  for  some  time,  occupied  the  mathema- 
ticians of  Europe,  whether  the  forces  of  bodies  in  motion 
should  be  reckoned  proportional  to  the  velocity,  or  to  the 
square  of  the  velocity.  We  need  not  here  recall  the 
events  of  this  dispute ;  but  we  may  remark,  that  its  his- 
tory, as  a  metaphysical  controversy,  is  remarkable  in  this 
respect,  that  it  has  been  finally  and  completely  settled ; 
for  it  is  now  agreed  among  mathematicians  that  both 
sides  were  right,  and  that  the  results  of  mechanical 
action  may  be  expressed  with  equal  correctness  by  means  of 
momentum  and  of  vis  viva*  It  is,  in  one  sense,  as  D'Alem- 
bert  has  saidf,  a  dispute  about  words;  but  we  are  not 
to  infer  that,  on  that  account,  it  was  frivolous  or  useless ; 
for  such  disputes  are  one  principal  means  of  reducing  the 
principles  of  our  knowledge  to  their  utmost  simplicity 
and  clearness.  The  terms  which  are  employed  in  the 
science  of  mechanics  are  now  liberated  for  ever,  in  the 
minds  of  mathematicians,  from  that  ambiguity  which  was 
the  battle-ground  in  the  war  of  the  vis  viva. 

But  we  may  observe  that  the  real  reason  of  this  con- 
troversy was  exactly  that  tendency  which  we  have  been 
noticing :  the  disposition  of  man  to  assume  in  his  specu- 
lations certain  general  propositions  as  true,  and  to  fix  the 
sense  of  terms  so  that  they  shall  fall  in  with  this  truth. 
It  was  agreed,  on  all  hands,  that  in  the  mutual  action  of 

*  Vol.  ii.  p.  87. 

f  D'Alembert  has  also  remarked  (Dynamique^  Pref.  xxi.,)  that 
this  controversy  "shows  how  little  justice  and  precision  there  is  in  the 
pretended  axiom  that  causes  are  proportional  to  their  effects."  But 
this  reflection  is  by  no  means  well  founded.  For  since  both  measures 
are  true,  it  appears  that  causes  may  \)QJiAStly  measured  by  their  effects, 
even  when  very  different  kinds  of  effects  are  taken.  That  the  axiom 
does  not  point  out  one  precise  measure  till  illustrated  by  experience  or 
by  other  considerations,  we  grant :  but  the  same  thing  occurs  in  the 
application  of  other  axioms  also. 


236          PHILOSOPHY  OF  THE  MECHANICAL  SCIENCES. 

bodies  the  same  quantity  of  force  is  always  preserved ; 
and  the  question  was,  by  which  of  the  two  measures  this 
rule  could  best  be  verified.  We  see,  therefore,  that  the 
dispute  was  not  concerning  a  definition  merely,  but  con- 
cerning a  definition  combined  with  a  general  proposition. 
Such  a  question  may  be  readily  conceived  to  have  been 
by  no  means  unimportant ;  and  we  may  remark,  in  pass- 
ing, that  such  controversies,  although  they  are  commonly 
afterwards  stigmatised  as  quarrels  about  words  and  defi- 
nitions, are,  in  reality,  events  of  considerable  conse- 
quence in  the  history  of  science ;  since  they  dissipate  all 
ambiguity  and  vagueness  in  the  use  of  terms,  and  bring 
into  view  the  conditions  under  which  the  fundamental 
principles  of  our  knowledge  can  be  most  clearly  and 
simply  presented. 

It  is  worth  our  while  to  pause  for  a  moment  on  the 
prospect  that  we  have  thus  obtained  of  the  advance  of 
knowledge,  as  exemplified  in  the  history  of  mechanics. 
The  general  transformation  of  our  views  from  vague  to 
definite,  from  complex  to  simple,  from  unexpected  dis- 
coveries to  self-evident  truths,  from  seeming  contradic- 
tions to  identical  propositions,  is  very  remarkable,  but  it 
is  by  no  means  peculiar  to  our  subject.  The  same  cir- 
cumstances, more  or  less  prominently,  more  or  less  deve- 
loped, appear  in  the  history  of  other  sciences,  according 
to  the  point  of  advance  which  each  has  reached.  They 
bear  upon  very  important  doctrines  respecting  the  pro- 
spects, the  limits,  and  the  very  nature  of  our  knowledge. 
And  though  these  doctrines  require  to  be  considered  with 
reference  to  the  whole  body  of  science,  yet  the  peculiar 
manner  in  which  they  are  illustrated  by  the  survey  of  the 
history  of  mechanics,  on  which  we  have  just  been  engaged, 
appears  to  make  this  a  convenient  place  for  introducing 
them  to  the  reader. 


237 


CHAPTER  VIII. 

OF    THE    PARADOX    OF    UNIVERSAL    PROPOSI- 
TIONS OBTAINED  FROM  EXPERIENCE. 

1.  IT  was  formerly  stated*  that  experience  cannot 
establish  any  universal  or  necessary  truths.  The  number 
of  trials  of  any  proposition  is  necessarily  limited,  and 
observation  alone  cannot  give  us  any  ground  of  extend- 
ing the  inference  to  untried  cases.  Observed  facts  have 
no  visible  bond  of  necessary  connexion,  and  no  exercise 
of  our  senses  can  enable  us  to  discover  such  connexion. 
We  can  never  acquire  from  a  mere  observation  of  facts, 
the  right  to  assert  that  a  proposition  is  true  in  all  cases, 
and  that  it  could  not  be  otherwise  than  we  find  it  to  be. 

Yet,  as  we  have  just  seen  in  the  history  of  the  laws  of 
motion,  we  may  go  on  collecting  our  knowledge  from 
observation,  and  enlarging  and  simplifying  it,  till  it  ap- 
proaches or  attains  to  complete  universality  and  seeming 
necessity.  Whether  the  laws  of  motion,  as  we  now  know 
them,  can  be  rigorously  traced  to  an  absolute  necessity  in 
the  nature  of  things,  we  have  not  ventured  absolutely  to 
pronounce.  But  we  have  seen  that  some  of  the  most 
acute  and  profound  mathematicians  have  believed  that 
for  these  laws  of  motion,  or  some  of  them,  there  was 
such  a  demonstrable  necessity  compelling  them  to  be 
such  as  they  are,  and  no  other.  Most  of  those  who  have 
carefully  studied  the  principles  of  mechanics  will  allow 
that  some  at  least  of  the  primary  laws  of  motion  approach 
very  near  to  this  character  of  necessary  truth ;  and  will 
confess  that  it  would  be  difficult  to  imagine  any  other 
consistent  scheme  of  fundamental  principles.  And  almost 
all  mathematicians  will  allow  to  these  laws  an  absolute 
universality ;  so  that  we  may  apply  them  without  scruple 

*  B.  i.,  c.  12.     Of  Experience. 


238  PHILOSOPHY  OF  THE  MECHANICAL  SCIENCES. 

or  misgiving,  in  cases  the  most  remote  from  those  to 
which  our  experience  has  extended.  What  astronomer 
would  fear  to  refer  to  the  known  laws  of  motion  in  rea- 
soning concerning  the  double  stars;  although  these  objects 
are  at  an  immeasurably  remote  distance  from  that  solar 
system  which  has  been  the  only  field  of  our  observation 
of  mechanical  facts  ?  What  philosopher,  in  speculating 
respecting  a  magnetic  fluid,  or  a  luminiferous  ether,  would 
hesitate  to  apply  to  it  the  mechanical  principles  which 
are  applicable  to  fluids  of  known  mechanical  properties  ? 
When  we  assert  that  the  quantity  of  motion  in  the  world 
cannot  be  increased  or  diminished  by  the  mutual  actions  of 
bodies,  does  not  every  mathematician  feel  convinced  that 
it  would  be  an  un philosophical  restriction  to  limit  this 
proposition  to  such  modes  of  action  as  we  have  tried  ? 

Yet  no  one  can  doubt  that,  in  historical  fact,  these 
laws  were  collected  from  experience.  That  such  is  the 
case,  is  no  matter  of  conjecture.  We  know  the  time,  the 
persons,  the  circumstances,  belonging  to  each  step  of  each 
discovery.  I  have,  in  the  History,  given  an  account  of 
these  discoveries;  and  in  the  previous  chapters  of  the 
present  work,  I  have  further  examined  the  nature  and 
the  import  of  the  principles  which  were  thus  brought  to 
light. 

Here,  then,  is  an  apparent  contradiction.  Experi- 
ence, it  would  seem,  has  done  that  which  we  had  proved 
that  she  cannot  do.  She  has  led  men  to  propositions, 
universal  at  least,  and  to  principles  which  appear  to  some 
persons  necessary.  What  is  the  explanation  of  this  con- 
tradiction, the  solution  of  this  paradox?  Is  it  true  that 
Experience  can  reveal  to  us  universal  and  necessary  truths? 
Does  she  possess  some  secret  virtue,  some  unsuspected 
power,  by  which  she  can  detect  connexions  and  conse- 
quences which  we  have  declared  to  be  out  of  her  sphere  ? 
Can  she  see  more  than  mere  appearances,  and  observe 


PARADOX    OF    UNIVERSAL    PROPOSITIONS.  239 

more  than  mere  facts?  Can  she  penetrate,  in  some  way, 
to  the  nature  of  things  ?  descend  below  the  surface  of 
phenomena  to  their  causes  and  origins,  so  as  to  be  able  to 
say  what  can  and  what  can  not  be ;  what  occurrences  are 
partial,  and  what  universal  ?  If  this  be  so,  we  have  in- 
deed mistaken  her  character  and  powers ;  and  the  whole 
course  of  our  reasoning  becomes  precarious  and  obscure. 
But,  then,  when  we  return  upon  our  path  we  cannot  find 
the  point  at  which  we  deviated,  we  cannot  detect  the 
false  step  in  our  deduction.  It  still  seems  that  by  expe- 
rience, strictly  so  called,  we  cannot  discover  necessary 
and  universal  truths.  Our  senses  can  give  us  no  evidence 
of  a  necessary  connexion  in  phenomena.  Our  observa- 
tion must  be  limited,  and  cannot  testify  concerning  any- 
thing which  is  beyond  its  limits.  A  general  view  of  our 
faculties  appears  to  prove  it  to  be  impossible  that  men 
should  do  what  the  history  of  the  science  of  mechanics 
shows  that  they  have  done. 

2.  But  in  order  to  try  to  solve  this  Paradox,  let  us 
again  refer  to  the  History  of  Mechanics.  In  the  cases 
belonging  to  that  science,  in  which  propositions  of  the 
most  unquestionable  universality,  and  most  approaching 
to  the  character  of  necessary  truths,  (as,  for  instance,  the 
laws  of  motion,)  have  been  arrived  at,  what  is  the  source 
of  the  axiomatic  character  which  the  propositions  thus 
assume  ?  The  answer  to  this  question  will,  we  may  hope, 
throw  some  light  on  the  perplexity  in  which  we  appear  to 
be  involved. 

Now  the  answer  to  this  inquiry  is,  that  the  laws  of 
motion  borrow  their  axiomatic  character  from  their 
being  merely  interpretations  of  the  Axioms  of  Causation. 
Those  axioms,  being  exhibitions  of  the  Idea  of  Cause 
under  various  aspects,  are  of  the  most  rigorous  univer- 
sality and  necessity.  And  so  far  as  the  laws  of  motion 
are  exemplifications  of  those  axioms,  these  laws  must  be 


240          PHILOSOPHY  OF  THE  MECHANICAL  SCIENCES. 

no  less  universal  and  necessary.  How  these  axioms  are 
to  be  understood ; — in  what  sense  cause  and  effect,  action 
and  reaction,  are  to  be  taken,  experience  and  observation 
did,  in  fact,  teach  inquirers  on  this  subject ;  and  without 
this  teaching,  the  laws  of  motion  could  never  have  been 
distinctly  known.  If  two  forces  act  together,  each  must 
produce  its  effect,  by  the  axiom  of  causation ;  and, 
therefore,  the  effects  of  the  separate  forces  must  be 
compounded.  But  a  long  course  of  discussion  and  experi- 
ment must  instruct  men  of  what  kind  this  composition  of 
forces  is.  Again ;  action  and  reaction  must  be  equal ; 
but  much  thought  and  some  trial  were  needed  to  show 
what  action  and  reaction  are.  Those  metaphysicians  who 
enunciated  Laws  of  motion  without  reference  to  expe- 
rience, propounded  only  such  laws  as  were  vague  and 
inapplicable.  But  yet  these  persons  manifested  the 
indestructible  conviction,  belonging  to  man's  speculative 
nature,  that  there  exist  Laws  of  motion,  that  is,  universal 
formulae,  connecting  the  causes  and  effects  when  motion 
takes  place.  Those  mechanicians,  again,  who  observed 
facts  involving  equilibrium  and  motion,  and  stated  some 
narrow  rules,  without  attempting  to  ascend  to  any 
universal  and  simple  principle,  obtained  laws  no  less 
barren  and  useless  than  the  metaphysicians ;  for  they 
could  not  tell  in  what  new  cases,  or  whether  in  any,  their 
laws  would  be  verified; — they  needed  a  more  general 
rule,  to  show  them  the  limits  of  the  rule  they  had  dis- 
covered. They  went  wrong  in  each  attempt  to  solve  a 
new  problem,  because  their  interpretation  of  the  terms  of 
the  axioms,  though  true,  perhaps,  in  certain  cases,  was 
not  right  in  general. 

Thus  Pappus  erred  in  attempting  to  interpret  as 
a  case  of  the  lever,  the  problem  of  supporting  a  weight 
upon  an  inclined  plane;  thus  Aristotle  erred  in  inter- 
preting the  doctrine  that  the  weight  of  bodies  is  the 


PARADOX  OF  UNIVERSAL  PROPOSITIONS.  241 

cause  of  their  fall ;  thus  Kepler  erred  in  interpreting  the 
rule  that  the  velocity  of  bodies  depends  upon  the  force ; 
thus  Bernoulli*  erred  in  interpreting  the  equality  of 
action  and  reaction  upon  a  lever  in  motion.  In  each  of 
these  instances,  true  doctrines,  already  established,  (whe- 
ther by  experiment  or  otherwise,)  were  erroneously  applied. 
And  the  error  was  corrected  by  further  reflection,  which 
pointed  out  that  another  mode  of  interpretation  was  requi- 
site, in  order  that  the  axiom  which  was  appealed  to  in 
each  case  might  retain  its  force  in  the  most  general  sense. 
And  in  the  reasonings  which  avoided  or  corrected  such 
errors,  and  which  led  to  substantial  general  truths,  the 
object  of  the  speculator  always  was  to  give  to  the  acknow- 
ledged maxims  which  the  Idea  of  Cause  suggested,  such 
a  signification  as  should  be  consistent  with  their  universal 
validity.  The  rule  was  not  accepted  as  particular  at  the 
outset,  and  afterwards  generalized  more  and  more  widely; 
but  from  the  very  first,  the  universality  of  the  rule  was 
assumed,  and  the  question  was,  how  it  should  be  under- 
stood so  as  to  be  universally  true.  At  every  stage  of 
speculation,  the  law  was  regarded  as  a  general  law.  This 
was  not  an  aspect  which  it  gradually  acquired,  by  the 
accumulating  contributions  of  experience,  but  a  feature 
of  its  original  and  native  character.  What  should 
happen  universally,  experience  might  be  needed  to  show: 
but  that  what  happened  should  happen  universally,  was 
implied  in  the  nature  of  knowledge.  The  universality  of 
the  laws  of  motion  was  not  gathered  from  experience, 
ijowever  much  the  laws  themselves  might  be  so. 

3.  Thus  we  obtain  the  solution  of  our  Paradox,  so 
far  as  the  case  before  us  is  concerned.  The  laws  of 
motion  borrow  their  form  from  the  Idea  of  Causation, 
though  their  matter  may  be  given  by  experience:  and 
hence  they  possess  a  universality  which  experience  cannot 

*  Hist,  Ind.  Sc.,  ii.  p.  83. 
VOL.  I.  R 


242          PHILOSOPHY  OF  THE  MECHANICAL  SCIENCES. 

give.  They  are  certainly  and  universally  valid ;  and  the 
only  question  for  observation  to  decide  is,  how  they  are 
to  be  understood.  They  are  like  general  mathematical 
formulae,  which  are  known  to  be  true  even  while  we  are 
ignorant  what  are  the  unknown  quantities  which  they 
involve.  It  must  be  allowed,  on  the  other  hand,  that  so 
long  as  these  formulae  are  not  interpreted  by  a  real  study 
of  nature,  they  are  not  only  useless  but  prejudicial,  filling 
men's  minds  with  vague  general  terms,  empty  maxims, 
and  unintelligible  abstractions,  which  they  mistake  for 
knowledge.  Of  such  perversion  of  the  speculative  pro- 
pensities of  man's  nature,  the  world  has  seen  too  much 
in  all  ages.  Yet  we  must  not,  on  that  account,  despise 
these  forms  of  truth,  since  without  them,  no  general 
knowledge  is  possible.  Without  general  terms,  and 
maxims,  and  abstractions,  we  can  have  no  science,  no 
speculation ;  hardly,  indeed,  consistent  thought  or  the 
exercise  of  reason.  The  course  of  real  knowledge  is,  to 
obtain  from  thought  and  experience  the  right  interpreta- 
tion of  our  general  terms,  the  real  import  of  our  maxims, 
the  true  generalizations  which  our  abstractions  involve. 

4.  If  it  be  asked,  how  experience  is  able  to  teach  us 
to  interpret  aright  the  general  terms  which  the  Axioms 
of  Causation  involve; — whence  she  derives  the  light 
which  she  is  to  throw  on  these  general  notions ;  the 
answer  is  obvious ; — namely,  that  the  relations  of  causa- 
tion are  the  conditions  of  experience  ; — that  the  general 
notions  are  exemplified  in  the  particular  cases  of  which 
she  takes  cognizance.  The  events  which  take  place 
about  us,  and  which  are  the  objects  of  our  observation, 
we  cannot  conceive  otherwise  than  as  subject  to  the 
laws  of  cause  and  effect.  Every  event  must  have  a 
cause ; — every  effect  must  be  determined  by  its  cause ; — 
these  maxims  are  true  of  the  phenomena  which  form  the 
materials  of  our  experience.  It  is  precisely  to  them, 


PARADOX  OF  UNIVERSAL  PROPOSITIONS.  243 

that  these  truths  apply.  It  is  in  the  world  which  we 
have  before  our  eyes,  that  these  propositions  are  univer- 
sally verified ;  and  it  is  therefore  by  the  observation  of 
what  we  see,  that  we  must  learn  how  these  propositions 
are  to  be  understood.  Every  fact,  every  experiment,  is 
an  example  of  these  statements ;  and  it  is  therefore  by 
attention  to  and  familiarity  with  facts  and  experiments, 
that  we  learn  the  signification  of  the  expressions  in  which 
the  statements  are  made ;  just  as  in  any  other  case  we 
learn  the  import  of  language  by  observing  the  manner  in 
which  it  is  applied  in  known  cases.  Experience  is  the 
interpreter  of  nature ;  it  being  understood  that  she  is  to 
make  her  interpretation  in  that  comprehensive  phraseo- 
logy which  is  the  genuine  language  of  science. 

5.  We  may  return  for  an  instant  to  the  objection, 
that  experience  cannot  give  us  general  truths,  since,  after 
any  number  of  trials  confirming  a  rule,  we  may,  for 
aught  we  can  foresee,  have  one  which  violates  the  rule. 
When  we  have  seen  a  thousand  stones  fall  to  the  ground, 
we  may  see  one  which  does  not  fall  under  the  same  appa- 
rent circumstances.  How  then,  it  is  asked,  can  experience 
teach  us  that  all  stones,  rigorously  speaking,  will  fall  if 
unsupported  ?  And  to  this  we  reply,  that  it  is  not  true 
that  we  can  conceive  one  stone  to  be  suspended  in  the 
air,  while  a  thousand  others  fall,  without  believing  some 
peculiar  cause  to  support  it ;  and  that,  therefore,  such  a 
supposition  forms  no  exception  to  the  law,  that  gravity  is 
a  force  by  which  all  bodies  are  urged  downwards.  Un- 
doubtedly we  can  conceive  a  body,  when  dropt  or  thrown, 
to  move  in  a  line  quite  different  from  other  bodies :  thus 
a  certain  missile  *  used  by  the  natives  of  Australia,  and 
lately  brought  to  this  country,  when  thrown  from  the 
hand  in  a  proper  manner,  describes  a  curve,  and  returns 
to  the  place  from  whence  it  was  thrown.  But  did  any 

*  Called  the  Bo*me-rang. 

R  2 


244         PHILOSOPHY    OF    THE    MECHANICAL    SCIENCES. 

one,  therefore,  even  for  an  instant  suppose  that  the  laws 
of  motion  are  different  for  this  and  for  other  bodies  ?  On 
the  contrary,  was  not  every  person  of  a  speculative  turn 
immediately  led  to  inquire  how  it  was  that  the  known 
causes  which  modify  motion,  the  resistance  of  the  air  and 
the  other  causes,  produced  in  this  instance  so  peculiar  an 
effect?  And  if  the  motion  had  been  still  more  unac- 
countable, it  would  not  have  occasioned  any  uncertainty 
whether  it  were  consistent  with  the  agency  of  gravity 
and  the  laws  of  motion.  If  a  body  suddenly  alter  its 
direction,  or  move  in  any  other  unexpected  manner,  \ve 
never  doubt  that  there  is  a  cause  of  the  change.  We 
may  continue  quite  ignorant  of  the  nature  of  this  cause, 
but  this  ignorance  never  occasions  a  moment's  doubt  that 
the  cause  exists  and  is  exactly  suited  to  the  effect.  And 
thus  experience  can  prove  or  discover  to  us  general 
rules,  but  she  can  never  prove  that  general  rules  do  not 
exist.  Anomalies,  exceptions,  unexplained  phenomena, 
may  remind  us  that  we  have  much  still  to  learn,  but  they 
can  never  make  us  suppose  that  truths  are  not  universal. 
We  may  observe  facts  that  show  us  we  have  not  fully 
understood  the  meaning  of  our  general  laws,  but  we  can 
never  find  facts  which  show  our  laws  to  have  no  meaning. 
Our  experience  is  bound  in  by  the  limits  of  cause  and 
effect,  and  can  give  us  no  information  concerning  any 
region  where  that  relation  does  not  prevail.  The  whole 
series  of  external  occurrences  and  objects,  through  all 
time  and  space,  exists  only,  and  is  conceived  only,  as 
subject  to  this  relation ;  and  therefore  we  endeavour 
in  vain  to  imagine  to  ourselves  when  and  where  and 
how  exceptions  to  this  relation  may  occur.  The  assump- 
tion of  the  connexion  of  cause  and  effect  is  essential  to 
our  experience,  as  the  recognition  of  the  maxims  which 
express  this  connexion  is  essential  to  our  knowledge. 
6.  I  have  thus  endeavoured  to  explain  in  some 


PARADOX  OF  UNIVERSAL  PROPOSITIONS.  245 

measure  how,  at  least  in  the  field  of  our  mechanical  know- 
ledge, experience  can  discover  universal  truths,  though 
she  cannot  give  them  their  universality ;  and  how  such 
truths,  though  borrowing  their  form  from  our  ideas,  cannot 
be  understood  except  by  the  actual  study  of  external 
nature.  And  thus  with  regard  to  the  laws  of  motion, 
and  other  fundamental  principles  of  Mechanics,  the 
analysis  of  our  ideas  and  the  history  of  the  progress  of 
the  science  well  illustrate  each  other. 

If  the  paradox  of  the  discovery  of  universal  truths  by 
experience  be  thus  solved  in  one  instance,  a  much  wider 
question  offers  itself  to  us ; — How  far  the  difficulty,  and 
how  far  the  solution,  are  applicable  to  other  subjects.  It 
is  easy  to  see  that  this  question  involves  most  grave  and 
extensive  doctrines  with  regard  to  the  whole  compass  of 
human  knowledge  :  and  the  views  to  which  we  have  been 
led  in  the  present  Book  of  this  work  are,  we  trust,  fitted 
to  throw  much  light  upon  the  general  aspect  of  the  sub- 
ject. But  after  discussions  so  abstract,  and  perhaps 
obscure,  as  those  in  which  we  have  been  engaged  for 
some  chapters,  I  willingly  postpone  to  a  future  occasion 
an  investigation  which  may  perhaps  appear  to  most 
readers  more  recondite  and  difficult  still.  And  we  have, 
in  fact,  many  other  special  fields  of  knowledge  to  survey, 
before  we  are  led  by  the  order  of  our  subject,  to  those 
general  questions  and  doctrines,  those  antitheses  brought 
into  view  and  again  resolved,  which  a  view  of  the  whole 
territory  of  human  knowledge  suggests,  and  by  which 
the  nature  and  conditions  of  knowledge  are  exhibited. 

Before  we  quit  the  subject  of  mechanical  science  we 
shall  make  a  few  remarks  on  another  doctrine  t  which 
forms  part  of  the  established  truths  of  the  science, 
namely,  the  doctrine  of  universal  gravitation, 


246 


CHAPTER  IX. 

OF  THE  ESTABLISHMENT  OF  THE  LAW  OF 
UNIVERSAL  GRAVITATION. 

THE  doctrine  of  universal  gravitation  is  a  feature  of 
so  much  importance  in  the  history  of  science  that  we 
shall  not  pass  it  by  without  a  few  remarks  on  the  nature 
and  evidence  of  the  doctrine. 

1.  To  a  certain  extent  the  doctrine  of  the  attraction 
of  bodies  according  to  the  law  of  the  inverse  square  of 
the  distance,  exhibits  in  its  progress  among  men  the  same 
general  features  which  we  have  noticed  in  the  history 
of  the  laws  of  motion.     This  doctrine  was  maintained 
a  priori  on  the  ground  of  its  simplicity,  and  asserted 
positively,  even  before  it  was  clearly  understood : — not- 
withstanding this  anticipation,  its  establishment  on  the 
ground  of  facts  was  a  task  of  vast  labour  and  sagacity : — 
when  it  had  been  so  established  in  a  general  way,  there 
occurred  at  later  periods,  an  occasional  suspicion  that  it 
might  be  approximately  true  only : — these  suspicions  led 
to  further  researches,  which  showed  the  rule  to  be  rigor- 
ously exact : — and  at  present  there  are  mathematicians 
who  maintain,  not  only  that  it  is  true,  but  that  it  is  a 
necessary  property  of  matter.     A  very  few  words  on  each 
of  these  points  will  suffice. 

2.  I  have  shown  in  the  History  of  Science*,  that  the 
attraction  of  the  sun  according  to  the  inverse  square  of 
the  distance,  had  been  divined  by  Bullialdus,  Hooke,  Hal- 
ley,  and  others,  before  it  was  proved  by  Newton.     Pro- 
bably the  reason  which  suggested  this  conjecture  was  that 
gravity  might  be  considered  as  a  sort  of  emanation ;  and 
that  thus,  like  light  or  any  other  effect  diffused  from  a 

*  Vol.  ii.,  148. 


ESTABLISHMENT  OF  UNIVERSAL  GRAVITATION.       247 

centre,  it  must  follow  the  law  just  stated,  the  efficacy  of 
the  force  being  weakened  in  receding  from  the  centre, 
exactly  in  proportion  to  the  space  througli  which  it  is 
diffused.  It  cannot  be  denied  that  such  a  view  appears 
to  be  strongly  recommended  by  analogy. 

When  it  had  been  proved  by  Newton  that  the  planets 
were  really  retained  in  their  elliptical  orbits  by  a  central 
force,  his  calculations  also  showed  that  the  above-stated 
law  of  the  force  must  be  at  least  very  approximately 
correct,  since  otherwise  the  aphelia  of  the  orbits  could 
not  be  so  nearly  at  rest  as  they  were.  Yet  when  it 
seemed  as  if  the  motion  of  the  moon's  apogee  could  not 
be  accounted  for  without  some  new  supposition,  the  a 
priori  argument  in  favour  of  the  inverse  square  did  not 
prevent  Clairaut  from  trying  the  hypothesis  of  a  small 
term  added  to  that  which  expressed  the  ancient  law :  but 
when,  in  order  to  test  the  accuracy  of  this  hypothesis,  the 
calculation  of  the  motion  of  the  moon's  apogee  was 
pushed  to  a  greater  degree  of  exactness  than  had  been 
obtained  before,  it  was  found  that  the  new  term  vanished 
of  itself;  and  that  the  inverse  square  now  accounted  for 
tke  whole  of  the  motion.  And  thus,  as  in  the  case  of 
the  second  law  of  motion,  the  most  scrupulous  examina- 
tion terminated  in  showing  the  simplest  rule  to  be  rigor- 
ously true. 

3.  Similar  events  occurred  in  the  history  of  another  part 
of  the  law  of  gravitation:  namely,  that  the  attraction  is  pro- 
portional to  the  quantity  of  matter  attracted.  This  part  of 
the  law  may  also  be  thus  stated,  That  the  weight  of  bodies 
arising  from  gravity  is  proportional  to  their  inertia ;  and 
thus,  that  the  accelerating  force  on  all  bodies  under  the 
same  circumstances  is  the  same.  Newton  made  experi- 
ments which  proved  this  with  regard  to  terrestrial  bodies ; 
for  he  found  that,  at  the  end  of  equal  strings,  balls  of .  all 
substances,  gold,  silver,  lead,  glass,  wood,  &c.,  oscillated 


248         PHILOSOPHY  OF  THE  MECHANICAL  SCIENCES. 

in  equal  times*.  But  a  few  years  ago,  doubts  arose 
among  the  German  astronomers  whether  this  law  was 
rigorously  true  with  regard  to  the  planetary  bodies. 
Some  calculations  appeared  to  prove,  that  the  attraction 
of  Jupiter  as  shown  by  the  perturbations  which  he  pro- 
duces in  the  small  planets  Juno,  Vesta,  and  Pallas,  was 
different  from  the  attraction  which  he  exerts  on  his 
own  satellites.  Nor  did  there  appear  to  these  philoso- 
phers anything  inconceivable  in  the  supposition  that  the 
attraction  of  a  planet  might  be  thus  elective.  But  when 
Mr.  Airy  obtained  a  more  exact  determination  of  the 
mass  of  Jupiter,  as  indicated  by  his  effect  on  his  satel- 
lites, it  was  found  that  this  suspicion  was  unfounded ; 
and  that  there  was,  in  this  case,  no  exception  to  the 
universality  of  the  rule,  that  this  cosmical  attraction  is  in 
the  proportion  of  the  attracted  mass. 

4.  Again :  when  it  had  thus  been  shown  that  a  mutual 
attraction  of  parts,  according  to  the  law  above  mentioned, 
prevailed  throughout  the  extent  of  the  solar  system,  it 
might  still  be  doubted  whether  the  same  law  extended 
to  other  regions  of  the  universe.  It  might  have  been 
perhaps  imagined  that  each  fixed  star  had  its  peculiar 
law  of  force.  But  the  examination  of  the  motions  of 
double  stars  about  each  other,  by  the  two  Herschels  and 
others,  appears  to  show  that  they  describe  ellipses  as  the 
planets  do :  and  thus  extends  the  law  of  the  inverse 
squares  to  parts  of  the  universe  immeasurably  distant 
from  the  whole  solar  system. 

5.  Since  every  doubt  which  lias  been  raised  with 
regard  to  the  universality  and  accuracy  of  the  law  of 
gravitation,  has  thus  ended  in  confirming  the  rule,  it  is 
not  surprising  that  men's  minds  should  have  returned 
with  additional  force  to  those  views  which  had  at  first 
represented  the  law  as  a  necessary  truth,  capable  of  being 

*  Princ,  1.  in,,  Prop.  6, 


ESTABLISHMENT  OF  UNIVERSAL  GRAVITATION.          249 

established  by  reason  alone.  When  it  had  been  proved 
by  Newton  that  gravity  is  really  a  universal  attribute  of 
matter  as  far  as  we  can  learn,  his  pupils  were  not  content 
without  maintaining  it  be  an  essential  quality.  This  is 
the  doctrine  held  by  Cotes  in  the  preface  to  the  second 
edition  of  the  Principia  (1712) :  "  Gravity,"  he  says,  "  is 
a  primary  quality  of  bodies,  as  extension,  mobility,  and 
impenetrability  are."  But  Newton  himself  by  no  means 
went  so  far.  In  his  second  Letter  to  Bentley  (1693),  he 
says :  "  You  sometimes  speak  of  gravity  as  essential  and 
inherent  to  matter ;  pray  do  not  ascribe  that  notion  to 
me.  The  cause  of  gravity,"  he  adds,  "I  do  not  pretend 
to  know,  and  would  take  more  time  to  consider  of  it." 

Cotes  maintains  his  opinion  by  urging,  that  we  learn 
by  experience  that  all  bodies  possess  gravity,  and  that  we 
do  not  learn  in  any  other  way  that  they  are  extended, 
moveable,  or  solid.  But  we  have  already  seen,  that  the 
ideas  of  space,  time,  and  reaction,  on  which  depend 
extension,  mobility,  and  solidity,  are  not  results,  but  con- 
ditions, of  experience.  We  cannot  conceive  a  body 
except  as  extended ;  we  cannot  conceive  it  to  exert 
mechanical  action  except  with  some  kind  of  solidity. 
But  so  far  as  our  conceptions  of  body  have  hitherto  been 
developed,  we  find  no  difficulty  in  conceiving  two  bodies 
which  do  not  attract  each  other. 

6.  Newton  lays  down,  in  the  second  edition  of  the 
Principia,  this  "  Rule  of  Philosophizing"  (Book  iii.) ;  that 
"  The  qualities  of  bodies  which  cannot  be  made  more  or 
less  intense,  and  which  belong  to  all  bodies  on  which  we 
are  able  to  make  experiments,  are  to  be  held  to  be  quali- 
ties of  all  bodies  in  general."  And  this  Rule  is  cited  in 
the  sixth  proposition  of  the  Third  Book  of  the  Principia, 
(Cor.  2,)  in  order  to  prove  that  gravity,  proportional  to 
the  quantity  of  matter,  may  be  asserted  to  be  a  quality  of 
all  bodies  universally,  But  we  may  remark  that  a  Rule 


250          PHILOSOPHY  OF  THE  MECHANICAL  SCIENCES. 

of  Philosophizing,  itself  of  precarious  authority,  cannot 
authorize  us  in  ascribing  universality  to  an  empirical 
result.  Geometrical  and  statical  properties  are  seen  to 
be  necessary,  and  therefore  universal :  but  Newton  appears 
disposed  to  assert  a  like  universality  of  gravity,  quite 
unconnected  with  any  necessity.  It  would  be  a  very 
inadequate  statement,  indeed  a  false  representation,  of 
statical  truth,  if  we  were  to  say,  that  because  every  body 
which  has  hitherto  been  tried  has  been  found  to  have  a 
centre  of  gravity,  we  venture  to  assert  that  all  bodies 
whatever  have  a  centre  of  gravity.  And  if  we  are  ever 
able  to  assert  the  absolute  universality  of  the  law  of  gra- 
vitation, we  shall  have  to  rest  this  truth  upon  the  clearer 
development  of  our  ideas  of  matter  and  force ;  not  upon  a 
Rule  of  Philosophizing,  which,  till  otherwise  proved,  must 
be  a  mere  rule  of  prudence,  and  which  the  opponent  may 
refuse  to  admit. 

7.  Other  persons,  instead  of  asserting  gravity  to  be 
in  its  own  nature  essential  to  matter,  have  made  hypo- 
theses concerning  some  mechanism  or  other,  by  which 
this  mutual  attraction  of  bodies  is  produced*.  Thus  the 
Cartesians  ascribed  to  a  vortex  the  tendency  of  bodies  to 
a  centre ;  Newton  himself  seems  to  have  been  disposed 
to  refer  this  tendency  to  the  elasticity  of  an  ether ;  Le 
Sage  propounded  a  curious  hypothesis,  in  which  this 
attraction  is  accounted  for  by  the  impulse  of  infinite 
streams  of  particles  flowing  constantly  through  the  uni- 
verse in  all  directions.  In  these  speculations,  the  force 
of  gravity  is  resolved  into  the  pressure  or  impulse  of 
solids  or  fluids.  On  the  other  hand,  hypotheses  have 
been  propounded,  in  which  the  solidity,  and  other  phy- 
sical qualities  of  bodies,  have  been  explained  by  repre- 
senting the  bodies  as  a  collection  of  points,  from  which 

*  See  VINCE,  Observations  on  the  Hypotheses  respecting  Gravitation^ 
and  the  Critique  of  that  vyork,  Edinb.  Rev,  vol,  xiii. 


ESTABLISHMENT  OF  UNIVERSAL  GRAVITATION.         251 

points  repulsive,  as  well  as  attractive,  forces  emanate. 
This  view  of  the  constitution  of  bodies  was  maintained 
and  developed  by  Boscovich,  and  is  hence  termed  "  Bos- 
covich's  Theory :"  and  the  discussion  of  it  will  more  pro- 
perly come  under  our  review  at  a  future  period,  when  we 
speak  of  the  question  whether  bodies  are  made  up  of 
atoms.  But  we  may  observe,  that  Newton  himself 
appears  to  have  inclined,  as  his  followers  certainly  did,  to 
this  mode  of  contemplating  the  physical  properties  of 
bodies.  In  his  Preface  to  the  Principia,  after  speaking 
of  the  central  forces  which  are  exhibited  in  cosmical  phe- 
nomena, he  says :  "  Would  that  we  could  derive  the 
other  phenomena  of  Nature  from  mechanical  principles 
by  the  same  mode  of  reasoning.  For  many  things  move 
me,  so  that  I  suspect  all  these  phenomena  may  depend 
upon  certain  forces,  by  which  the  particles  of  bodies, 
through  causes  not  yet  known,  are  either  impelled  to 
each  other  and  cohere  according  to  regular  figures,  or  are 
repelled  and  recede  from  each  other :  which  forces  being 
unknown,  philosophers  have  hitherto  made  their  attempts 
upon  nature  in  vain." 

8.  But  both  these  hypotheses ; — that  by  which  cohe- 
sion and  solidity  are  reduced  to  attractive  and  repulsive 
forces,  and  that  by  which  attraction  is  reduced  to  the 
impulse  and  pressure  of  media; — are  hitherto  merely 
modes  of  representing  mechanical  laws  of  nature ;  and 
cannot,  either  of  them,  be  asserted  as  possessing  any  evi- 
dent truth  or  peremptory  authority  to  the  exclusion  of 
the  other.  This  consideration  may  enable  us  to  estimate 
the  real  weight  of  the  difficulty  felt  in  assenting  to  the 
mutual  attraction  of  bodies  not  in  contact  with  each 
other ;  for  it  is  often  urged  that  this  attraction  of  bodies 
at  a  distance  is  an  absurd  supposition. 

The  doctrine  is  often  thus  stigmatised,  both  by  popu- 
lar and  by  learned  writers.  It  was  long  received  as  a 


252          PHILOSOPHY  OF  THE  MECHANICAL  SCIENCES. 

maxim  in  philosophy  (as  Monboddo  informs  us*),  that  a 
body  cannot  act  where  it  is  not,  any  more  than  when  it  is 
not.  But  to  this  we  reply,  that  time  is  a  necessary  con- 
dition of  our  conception  of  causation,  in  a  different  man- 
ner from  space.  The  action  of  force  can  only  be  con- 
ceived as  taking  place  in  a  succession  of  moments,  in 
each  of  which  cause  and  effect  immediately  succeed  each 
other:  and  thus  the  interval  of  time  between  a  cause  and 
its  remote  effect  is  filled  up  by  a  continuous  succession  of 
events  connected  by  the  same  chain  of  causation.  But 
in  space,  there  is  no  such  visible  necessity  of  continuity; 
the  action  and  reaction  may  take  place  at  a  distance  from 
each  other;  all  that  is  necessary  being  that  they  be  equal 
and  opposite. 

Undoubtedly  the  existence  of  attraction  is  rendered 
more  acceptable  to  common  apprehension  by  supposing 
some  intermediate  machinery, — a  cord,  or  rod,  or  fluid, — 
by  which  the  forces  may  be  conveyed  from  one  point  to 
another.  But  such  images  are  rather  fitted  to  satisfy 
those  prejudices  which  arise  from  the  earlier  applica- 
tion of  our  ideas  of  force,  than  the  real  nature  of  those 
ideas.  If  we  suppose  two  bodies  to  pull  each  other  by 
means  of  a  rod  or  a  cord,  we  only  suppose,  in  addition  to 
those  equal  and  opposite  forces  acting  upon  the  two 
bodies,  which  forces  are  alone  essential  to  mutual  attrac- 
tion, a  certain  power  of  resisting  transverse  pressure  at 
every  point  of  the  intermediate  line :  which  additional 
supposition  is  entirely  useless,  and  quite  unconnected 
with  the  essential  conditions  of  the  case.  When  the 
Newtonians  were  accused  of  introducing  into  philosophy 
an  unknown  cause  which  they  termed  attraction,  they 
justly  replied  that  they  knew  as  much  respecting  attrac- 
tion as  their  opponents  did  about  impulse.  In  each  case 
we  have  a  knowledge  of  the  conception  in  question  so 

*  Ancient  Metaphysics,  vol.  ii.  p.  175, 


ESTABLISHMENT  OF  UNIVERSAL  GRAVITATION.         253 

far  as  we  clearly  apprehend  it  under  the  conditions  of 
those  axioms  of  mechanical  causation  which  form  the 
basis  of  our  science  on  such  subjects. 

Having  thus  examined  the  degree  of  certainty  and 
generality  to  which  our  knowledge  of  the  law  of  universal 
gravitation  has  been  carried,  by  the  progress  of  mechanical 
discovery  and  speculation  up  to  the  present  time,  we 
might  proceed  to  the  other  branches  of  science,  and 
examine  in  like  manner  their  grounds  and  conditions. 
But  before  we  do  this,  it  will  be  worth  our  while  to 
attend  for  a  moment  to  the  effect  which  the  progress  of 
mechanical  ideas  among  mathematicians  and  mechanical 
philosophers  has  produced  upon  the  minds  of  other  per- 
sons, who  share  only  in  an  indirect  and  derivative  manner 
in  the  influence  of  science. 


CHAPTER  X. 

OF    THE    GENERAL    DIFFUSION    OF    CLEAR 
MECHANICAL  IDEAS. 

1.  WE  have  seen  how  the  progress  of  knowledge 
upon  the  subject  of  motion  and  force  has  produced,  in 
the  course  of  the  world's  history,  a  great  change  in  the 
minds  of  acute  and  speculative  men ;  so  that  such  per- 
sons can  now  reason  with  perfect  steadiness  and  precision 
upon  subjects  on  which,  at  first,  their  thoughts  were  vague 
and  confused ;  and  can  apprehend,  as  truths  of  complete 
certainty  and  evidence,  laws  which  it  required  great  labour 
and  time  to  discover.  This  complete  developement  and 
clear  manifestation  of  mechanical  ideas  has  taken  place 
only  among  mathematicians  and  philosophers.  But  yet  a 
progress  of  thought  upon  such  subjects  ;  an  advance  from 
the  obscure  to  the  clear,  and  from,  error  to  truth  ;  may  be 


254  PHILOSOPHY  OF  THE  MECHANICAL  SCIENCES. 

traced  in  the  world  at  large,  and  among  those  who  have 
not  directly  cultivated  the  exact  sciences.  This  diffused 
and  collateral  influence  of  science  manifests  itself, 
although  in  a  wavering  and  fluctuating  manner,  by  vari- 
ous indications,  at  various  periods  of  literary  history. 
The  opinions  and  reasonings  which  are  put  forth  upon 
mechanical  subjects,  and  above  all,  the  adoption  into  com- 
mon language,  of  terms  and  phrases  belonging  to  the 
prevalent  mechanical  systems,  exhibit  to  us  the  most  pro- 
found discoveries  and  speculations  of  philosophers  in 
their  effect  upon  more  common  and  familiar  trains  of 
thought.  This  effect  is  by  no  means  unimportant,  and 
we  shall  point  out  some  examples  of  such  indications  as 
we  have  mentioned. 

2.  The  discoveries  of  the  ancients  in  speculative 
mechanics  were,  as  we  have  seen,  very  scanty  ;  and  hardly 
extended  their  influence  to  the  unmathematical  world. 
Yet  the  familiar  use  of  the  term  "  centre  of  gravity" 
preserved  and  suggested  the  most  important  part  of  what 
the  Greeks  had  to  teach.  The  other  phrases  which  they 
employed,  as  momentum,  energy,  virtue,  force,  and  the 
like,  never  had  any  exact  meaning,  even  among  mathe- 
maticians ;  and  therefore  never,  in  the  ancient  world,  be- 
came the  means  of  suggesting  just  habits  of  thought.  I 
have  pointed  out,  in  the  History  of  Science,  several  cir- 
cumstances which  appear  to  denote  the  general  confusion 
of  ideas  which  prevailed  upon  mechanical  subjects  during 
the  times  of  the  Roman  empire.  I  have  there  taken  as 
one  of  the  examples  of  this  confusion,  the  fable  narrated 
by  Pliny  and  others  concerning  the  echine'js,  a  small 
fish,  which  was  said  to  stop  a  ship  merely  by  sticking 
to  it*.  This  story  was  adduced  as  betraying  the  absence 
of  any  steady  apprehension  of  the  equality  of  action  and 
reaction ;  since  the  fish,  except  it  had  some  immoveable 
*  Hist.  Ind.  Scl,  i.  245. 


DIFFUSION  OF  CLEAR  MECHANICAL  IDEAS.  255 

obstacle  to  hold  by,  must  be  pulled  forward  by  the  ship, 
as  much  as  it  pulled  the  ship  backward.  If  the  writers 
who  speak  of  this  wonder  had  shown  any  perception  of 
the  necessity  of  a  reaction,  either  produced  by  the  rapid 
motion  of  the  fish's  fins  in  the  water,  or  in  any  other  way, 
they  would  not  be  chargeable  with  this  confusion  of 
thought ;  but  from  their  expressions  it  is,  I  think,  evident 
that  they  saw  no  such  necessity*.  Their  idea  of  mecha- 
nical action  was  not  sufficiently  distinct  to  enable  them 
to  see  the  absurdity  of  supposing  an  intense  pressure  with 
no  obstacle  for  it  to  exert  itself  against. 

3.  We  may  trace,  in  more  modern  times  also,  indica- 
tions of  a  general  ignorance  of  mechanical  truths.  Thus 
the  phrase  of  shooting  at  an  object  "  point-blank,"  im- 
plies the  belief  that  a  cannon-ball  describes  a  path  of 
which  the  first  portion  is  a  straight  line.  This  error  was 
corrected  by  the  true  mechanical  principles  which  Galileo 
and  his  followers  brought  to  light ;  but  these  principles 
made  their  way  to  popular  notice,  principally  in  conse- 
quence of  their  application  to  the  motions  of  the  solar 
system,  and  to  the  controversies  which  took  place  respect- 
ing those  motions.  Thus  by  far  the  most  powerful  argu- 
ment against  the  reception  of  the  Copernican  system  of 
the  universe,  was  that  of  those  who  asked,  Why  a  stone 
dropt  from  a  tower  was  not  left  behind  by  the  motion  of 
the  earth  ?  The  answer  to  this  question,  now  universally 

*  See  Prof.  POWELL  On  the  Nature  and  Evidence  of  the  Laws  of 
Motion.  Reports  of  the  Ashmolean  Society.  Oxford.  1837.  Professor 
Powell  has  made  an  objection  to  my  use  of  this  instance  of  confusion 
of  thought;  the  remark  in  the  text  seems  to  me  to  justify  what  I  said 
in  the  History.  As  an  evidence  that  the  fish  was  not  supposed  to  pro- 
duce its  effect  by  its  muscular  power  acting  on  the  water,  we  may  take 
what  Pliny  says,  Nat.  Hist.)  xxxii.  1,  <{  Domat  niundi  rabiem,  nullo 
suo  labore;  non  retinendo,  aut  alio  modo  quam  adhserendo  :"  and  also 
what  he  states  in  another  place  (ix.  41,)  that  when  it  is  preserved  in 
pickle,  it  may  be  used  in  recovering  gold  which  has  fallen  into  a  deep 
well.  All  this  implies  adhesion  alone,  with  no  conception  of  reaction. 


256  PHILOSOPHY  OF  THE  MECHANICAL  SCIENCES. 

familiar,  involves  a  reference  to  the  true  doctrine  of  the 
composition  of  motions.      Again;    Kepler's  persevering 
and  strenuous  attempts*  to  frame  a  physical  theory  of 
the  universe  were  frustrated  by  his  ignorance  of  the  first 
law  of  motion,  which  informs  us  that  a  body  will  retain 
its  velocity  without  any  maintaining  force.    He  proceeded 
upon  the  supposition  that  the  sun's  force  was  requisite  to 
keep  up  the  motion  of  the  planets,  as  well  as  to  deflect  and 
modify  it ;  and  he  was  thus  led  to  a  system  which  repre- 
sented the  sun  as  carrying  round  the  planets  in  their 
orbits  by  means  of  a  vortex,  produced  by  his  revolution. 
The  same  neglect  of  the  laws  of  motion  presided  in  the 
formation  of  Descartes'  system  of  vortices.      Although 
Descartes  had  enunciated  in  words  the  laws  of  motion, 
he  and  his  followers  showed  that  they  had  not  the  practi- 
cal habit  of  referring  to  these  mechanical  principles ;  and 
dared  not  trust  the  planets  to  move  in  free  space  without 
some  surrounding  machinery  to  support  themf. 

4.  When  at  last  mathematicians,  following  Newton, 
had  ventured  to  consider  the  motion  of  each  planet  as  a 
mechanical  problem  not  different  in  its  nature  from  the 
motion  of  a  stone  cast  from  the  hand ;  and  when  the 
solution  of  this  problem  and  its  immense  consequences 
had  become  matters  of  general  notoriety  and  interest ; 
the  new  views  introduced,  as  is  usual,  new  terms,  which 
soon  became  extensively  current.  We  meet  with  such 
phrases  as  "  flying  off  in  the  tangent,"  and  "  deflexion 
from  the  tangent ;"  with  antitheses  between  "centripetal" 
and  "  centrifugal  force,"  or  between  "  projectile"  and 
"  central  force."  "  Centres  of  force,"  "  disturbing  forces," 

*  Hist.  Ind.  Sci.,  i.  408;  ii.  129. 

t  I  have,  in  the  History,  applied  to  Descartes  the  character  which 
Bacon  gives  to  Aristotle,  "  Audax  simul  et  pavidus :''  though  he  was 
bold  enough  to  enunciate  the  laws  of  motion  without  knowing  them 
aright,  he  had  not  the  courage  to  leave  the  planets  to  describe  their 
orbits  by  the  agency  of  those  laws,  without  the  machinery  of  contact. 


DIFFUSION  OF  CLEAR  MECHANICAL    IDEAS.  257 

"perturbations,"  and  "perturbations  of  higher  orders," 
are  not  unfrequently  spoken  of:  and  the  expression  "  to 
gravitate,"  and  the  term  "  universal  gravitation,"  acquired 
a  permanent  place  in  the  language. 

Yet  for  a  long  time,  and  even  up  to  the  present  day, 
we  find  many  indications  that  false  and  confused  appre- 
hensions on  such  subjects  are  by  no  means  extirpated. 
Arguments  are  urged  against  the  mechanical  system  of 
the  universe,  implying  in  the  opponents  an  absence  of  all 
clear  mechanical  notions.  Many  of  this  class  of  writers 
retrograde  to  Kepler's  point  of  view.  This  is,  for  example, 
the  case  with  Lord  Monboddo,  who,  arguing  on  the  as- 
sumption that  force  is  requisite  to  maintain,  as  well  as  to 
deflect  motion,  produced  a  series  of  attacks  upon  the 
Newtonian  philosophy;  which  he  inserted  in  his  Ancient 
Metaphysics,  published  in  1779  and  the  succeeding  years. 
This  writer  (like  Kepler),  measures  force  by  the  velocity 
which  the  body  has  *,  not  by  that  which  it  gains.  Such  a 
use  of  language  would  prevent  our  obtaining  any  laws  of 
motion  at  all.  Accordingly,  the  author,  in  the  very  next 
page  to  that  which  I  have  just  quoted,  abandons  this  mea- 
sure of  force,  and,  in  curvilinear  motion,  measures  force 
by  "  the  fall  from  the  extremity  of  the  arc."  Again ;  in 
his  objections  to  the  received  theory,  he  denies  that  cur- 
vilinear motion  is  compounded,  although  his  own  mode  of 
considering  such  motion  assumes  this  composition  in  the 
only  way  in  which  it  was  ever  intended  by  mathema- 
ticians. Many  more  instances  might  be  adduced  to  show 
that  a  want  of  cultivation  of  the  mechanical  ideas  ren- 
dered this  philosopher  incapable  of  judging  of  a  mecha- 
nical system. 

The  following  extract  from  the  Ancient  Metaphy- 
sics9  may  be  sufficient  to  show  the  value  of  the  author's 
criticism  on  the  subjects  of  which  we  are  now  speaking. 

*  Am.  Met.,  vol.  ii.,  b.  v.,  c.  6.,  p.  413. 
VOL.  I.  S 


258  PHILOSOPHY  OF  THE  MECHANICAL  SCIENCES. 

His  object  is  to  prove  that  there  do  not  exist  a  centripetal 
and  a  centrifugal  force  in  the  case  of  elliptical  motion. 
"  Let  any  man  move  in  a  circular  or  elliptical  line  described 
to  him ;  and  he  will  find  no  tendency  in  himself  either 
to  the  centre  or  from  it,  much  less  both.  If  indeed  he 
attempt  to  make  the  motion  with  great  velocity,  or  if  he 
do  it  carelessly  and  inattentively,  he  may  go  out  of  the 
line,  either  towards  the  centre  or  from  it :  but  this  is  to 
be  ascribed,  not  to  the  nature  of  the  motion,  but  to  our 
infirmity ;  or  perhaps  to  the  animal  form,  which  is  more 
fitted  for  progressive  motion  in  a  right  line  than  for  any 
kind  of  curvilinear  motion.  But  this  is  not  the  case  with 
a  sphere  or  spheroid,  which  is  equally  adapted  to  motion 
in  all  directions*."  We  need  hardly  remind  the  reader 
that  the  manner  in  which  a  man  running  round  a  small 
circle,  finds  it  necessary  to  lean  inwards,  in  order  that 
there  may  be  a  centripetal  inclination  to  counteract  the 
centrifugal  force,  is  a  standard  example  of  our  mechanical 
doctrines  ;  and  this  fact  (quite  familiar  in  practice  as  well 
as  theory,)  is  in  direct  contradiction  of  Lord  Monboddo's 
assertion. 

5.  A  similar  absence  of  distinct  mechanical  thought 
appears  in  some  of  the  most  celebrated  metaphysicians 
of  Germany.  I  have  elsewhere  noted  f  the  opinion  ex- 
pressed by  Hegel,  that  the  glory  which  belongs  to  Kepler 
has  been  unjustly  transferred  to  Newton ;  and  I  have 
Suggested,  as  the  explanation  of  this  mode  of  thinking, 
that  Hegel  himself,  in  the  knowledge  of  mechanical 
truth,  had  not  advanced  beyond  Kepler's  point  of  view. 
Persons  who  possess  conceptions  of  space  and  number, 
but  who  have  not  learnt  to  deal  with  ideas  of  force  and 
causation,  may  see  more  value  in  the  discoveries  of  Kepler 
than  in  those  of  Newton.  Another  exemplification  of  this 

*  Anc.  Met.,  vol.  i.,  b.  ii.,  c.  19,  p.  264. 
t  Hist.  Ind.  Sc.,  ii.,  181. 


DIFFUSION  OF  CLEAR  MECHANICAL  IDEAS.  259 

state  of  mind  may  be  found  in  Mr.  Schelling's  specula- 
tions ;  for  instance,  in  his  Lectures  on  the  Method  of  Aca- 
demical Study.  In  the  twelfth  Lecture,  on  the  Study  of 
Physics  and  Chemistry,  he  says,  (p.  266,)  "  What  the 
mathematical  natural  philosophy  has  done  for  the  know- 
ledge of  the  laws  of  the  universe  since  the  time  that  they 
were  discovered  by  his  (Kepler's)  godlike  genius,  is,  as 
is  well  known,  this :  it  has  attempted  a  construction  of 
those  laws  which,  according  to  its  foundations,  is  altoge- 
ther empirical.  We  may  assume  it  as  a  general  rule,  that 
in  any  proposed  construction,  that  which  is  not  a  pure 
general  form  cannot  have  any  scientific  import  or  truth. 
The  foundation  from  which  the  centrifugal  motion  of  the 
bodies  of  the  world  is  derived,  is  no  necessary  form,  it  is 
an  empirical  fact.  The  Newtonian  attractive  force,  even 
if  it  be  a  necessary  assumption  for  a  merely  reflective 
view  of  the  subject,  is  still  of  no  significance  for  the 
Reason,  which  recognises  only  absolute  relations.  The 
grounds  of  the  Keplerian  laws  can  be  derived,  without 
any  empirical  appendage,  purely  from  the  doctrine  of 
Ideas,  and  of  the  two  Unities,  which  are  in  themselves 
one  Unity,  and  in  virtue  of  which  each  being,  while  it  is 
absolute  in  itself,  is  at  the  same  time  in  the  absolute,  and 
reciprocally." 

It  will  be  observed,  that  in  this  passage  our  mecha- 
nical laws  are  objected  to  because  they  are  not  necessary 
results  of  our  ideas ;  which,  however,  as  we  have  seen, 
according  to  the  opinion  of  some  eminent  mechanical 
philosophers,  they  are.  But  to  assume  this  evident 
necessity  as  a  condition  of  every  advance  in  science,  is 
to  mistake  the  last,  perhaps  unattainable  step,  for  the 
first,  which  lies  before  our  feet.  And,  without  inquiring 
further  about  "  the  Doctrine  of  the  two  Unities,"  or  the 
manner  in  which  from  that  doctrine  we  may  deduce  the 
Keplerian  laws,  we  may  be  well  convinced  that  such  a 

s  2 


2GO        PHILOSOPHY    OF    THE    MECHANICAL    SCIENCES. 

doctrine  cannot  supply  any  sufficient  reason  to  induce  us 
to  quit  the  inductive  path  by  which  all  scientific  truth 
up  to  the  present  time  has  been  acquired. 

C.  But  without  going-  to  schools  of  philosophy  oppo- 
sed to  the  Inductive  School,  we  may  find  many  loose  and 
vague  habits  of  thinking  on  mechanical  subjects  among 
the  common  classes  of  readers  and  reasoners.  And  there 
are  some  familiar  modes  of  employing  the  phraseology  of 
mechanical  science,  which  are,  in  a  certain  degree,  charge- 
able with  inaccuracy,  and  may  produce  or  perpetuate 
confusion.  Among  such  cases  we  may  mention  the  way 
in  which  the  centripetal  and  centrifugal  forces,  and  also 
the  projectile  and  central  forces  of  the  planets,  are  often 
compared  or  opposed.  Such  antitheses  sometimes  pro- 
ceed upon  the  false  notion  that  the  two  members  of  these 
pairs  of  forces  are  of  the  same  kind  :  whereas  on  the 
contrary  the  projectile  force  is  a  hypothetical  impulsive 
force  which  may,  at  some  former  period,  have  caused  the 
motion  to  begin  ;  while  the  central  force  is  an  actual 
force,  which  must  act  continuously  and  during  the  whole 
time  of  the  motion,  in  order  that  the  motion  may  go  on 
in  the  curve.  In  the  same  manner  the  centrifugal  force 
is  not  a  distinct  force  in  a  strict  sense,  but  only  a  certain 
result  of  the  first  law  of  motion,  measured  by  the  portion 
of  centripetal  force  which  counteracts  it.  Comparisons 
of  quantities  so  heterogenous  imply  confusion  of  thought, 
and  often  suggest  baseless  speculations  and  imagined 
reforms  of  the  received  opinions. 

7.  I  might  point  out  other  terms  and  maxims,  in 
addition  to  those  already  mentioned,  which,  though  for- 
merly employed  in  a  loose  and  vague  manner,  are  now 
accurately  understood  and  employed  by  all  just  thinkers; 
and  thus  secure  and  diffuse  a  right  understanding  of 
mechanical  truths.  Such  are  momentum,  inertia,  quantity 
of  matter,  quantity  of  motion  ;  that  force  is  proportional 


DIFFUSION  OF  CLEAR  MECHANICAL  IDEAS.  201 

to  its  effects  ;  that  action  and  reaction  are  equal;  that  what 
is  gained  in  force  by  machinery  is  lost  in  time ;  that  the 
quantity  of  motion  in  the  world  cannot  be  either  increased 
or  diminished.  When  the  expression  of  the  truth  thus 
becomes  easy  and  simple,  clear  and  convincing,  the  mean- 
ings given  to  words  and  phrases  by  discoverers  glide  into 
the  habitual  texture  of  men's  reasonings,  and  the  effect  of 
the  establishment  of  true  mechanical  principles  is  felt  far 
from  the  school  of  the  mechanician.  If  these  terms  and 
maxims  are  understood  with  tolerable  clearness,  they 
carry  the  influence  of  truth  to  those  who  have  no  direct 
access  to  its  sources.  Many  an  extravagant  project  in 
practical  machinery,  and  many  a  wild  hypothesis  in  spe- 
culative physics,  has  been  repressed  by  the  general  cur- 
rency of  such  maxims  as  we  have  just  quoted. 

8.  Indeed  so  familiar  and  evident  are  the  elementary 
truths  of  mechanics  when  expressed  in  this  simple  form, 
that  they  are  received  as  truisms  ;  and  men  are  disposed 
to  look  back  with  surprise  and  scorn  at  the  speculations 
which  were  carried  on  in  neglect  of  them.  The  most 
superficial  reasoner  of  modern  times  thinks  himself  enti- 
tled to  speak  with  contempt  and  ridicule  of  Kepler's 
hypothesis  concerning  the  physical  causes  of  the  celestial 
motions:  and  gives  himself  credit  for  intellectual  supe- 
riority, because  he  sees,  as  self-evident,  what  such  a  man 
could  not  discover  at  all.  It  is  well  for  such  a  person  to 
recollect,  that  the  real  cause  of  his  superior  insight  is  not 
the  pre-eminence  of  his  faculties,  but  the  successful 
labours  of  those  who  have  preceded  him.  The  language 
which  he  has  learnt  to  use  unconsciously,  has  been  adapted 
to,  and  moulded  on,  ascertained  truths.  When  he  talks 
familiarly  of  accelerating  forces,  and  deflexions  from  the 
tangent,  he  is  assuming  that  which  Kepler  did  not  know, 
and  which  it  cost  Galileo  and  his  disciples  so  much  labour 
and  thought  to  establish.  Language  is  often  e$llfd  an 


262         PHILOSOPHY    OF   THE   MECHANICAL    SCIENCES. 

instrument  of  thought ;  but  it  is  also  the  nutriment  of 
thought ;  or  rather,  it  is  the  atmosphere  in  which  thought 
lives  :  a  medium  essential  to  the  activity  of  our  specu- 
lative power,  although  invisible  and  imperceptible  in  its 
operation ;  and  an  element  modifying,  by  its  qualities  and 
changes,  the  growth  and  complexion  of  the  faculties 
which  it  feeds.  In  this  way  the  influence  of  preceding- 
discoveries  upon  subsequent  ones,  of  the  past  upon  the 
present,  is  most  penetrating  and  universal,  though  most 
subtle  and  difficult  to  trace.  The  most  familiar  words 
and  phrases  are  connected  by  imperceptible  ties  with  the 
reasonings  and  discoveries  of  former  men  and  distant 
times.  Their  knowledge  is  an  inseparable  part  of  ours ; 
the  present  generation  inherits  and  uses  the  scientific 
wealth  of  all  the  past.  And  this  is  the  fortune,  not  only 
of  the  great  and  rich  in  the  intellectual  world :  of  those 
who  have  the  key  to  the  ancient  storehouses,  and  who 
have  accumulated  treasures  of  their  own ; — but  the 
humblest  inquirer,  while  he  puts  his  reasonings  into 
words,  benefits  by  the  labours  of  the  greatest  discoverers. 
When  he  counts  his  little  wealth,  he  finds  that  he  has  in 
his  hands  coins  which  bear  the  image  and  superscription  of 
ancient  and  modern  intellectual  dynasties ;  and  that  in 
virtue  of  this  possession,  acquisitions  are  in  his  power, 
solid  knowledge  within  his  reach,  which  none  could  ever 
have  attained  to,  if  it  were  not  that  the  gold  of  truth, 
once  dug  out  of  the  mine,  circulates  more  and  more 
widely  among  mankind. 

9.  Having  so  fully  examined,  in  the  preceding  in- 
stances, the  nature  of  the  progress  of  thought  which 
science  implies,  both  among  the  peculiar  cultivators  of 
science,  and  in  that  wider  world  of  general  culture  which 
receives  only  an  indirect  influence  from  scientific  disco- 
veries, we  shall  not  find  it  necessary  to  go  into  the  same 
extent  of  detail  with  regard  to  the  other  provinces  of 


DIFFUSION  OF  CLEAR   MECHANICAL  IDEAS.  263 

human  knowledge.  In  the  case  of  the  Mechanical  Sci- 
ences, we  have  endeavoured  to  show,  not  only  that  Ideas 
are  requisite  in  order  to  form  into  a  science  the  Facts 
which  nature  offers  to  us,  but  that  we  can  advance,  almost 
or  quite,  to  a  complete  identification  of  the  Facts  with 
the  Ideas.  In  the  sciences  to  which  we  now  proceed,  we 
shall  not  seek  to  fill  up  the  chasm  by  which  Facts  and 
Ideas  are  separated;  but  we  shall  endeavour  to  detect 
the  Ideas  which  our  knowledge  involves,  to  show  how 
essential  these  are ;  and  in  some  respects  to  trace  the 
mode  in  which  they  have  been  gradually  developed  among 
men. 

10.  The  motions  of  the  heavenly  bodies,  their  laws, 
their  causes,  are  among  the  subjects  of  the  first  division 
of  the  Mechanical  Sciences ;  and  of  these  sciences  we 
formerly  sketched  the  history,  and  have  now  endeavoured 
to  exhibit  the  philosophy.  If  we  were  to  take  any  other 
class  of  motions,  their  laws  and  causes  might  give  rise  to 
sciences  which  would  be  mechanical  sciences  in  exactly 
the  same  sense  in  which  Physical  Astronomy  is  so.  The 
phenomena  of  magnets,  of  electrical  bodies,  of  galvanical 
apparatus,  seem  to  form  obvious  materials  for  such  sci- 
ences ;  and  if  they  were  so  treated,  the  philosophy  of 
such  branches  of  knowledge  would  naturally  come  under 
our  consideration  at  this  point  of  our  progress. 

But  on  looking  more  attentively  at  the  sciences  of 
Electricity,  Magnetism,  and  Galvanism,  we  discover  cogent 
reasons  for  transferring  them  to  another  part  of  our 
arrangement ;  we  find  it  advisable  to  associate  them  with 
Chemistry,  and  to  discuss  their  principles  when  we  can 
connect  them  with  the  principles  of  chemical  science.  For 
though  the  first  steps  and  narrower  generalizations  of 
these  sciences  depend  upon  mechanical  ideas,  the  highest 
laws  and  widest  generalizations  which  we  can  reach 
respecting  them,  involve  chemical  relations.  The  pro- 


264  PHILOSOPHY  OF  THE  MECHANICAL  SCIENCES. 

gress  of  these  portions  of  knowledge  is  in  some  respects 
opposite  to  the  progress  of  Physical  Astronomy.  In 
this,  we  begin  with  phenomena  which  appear  to  indicate 
peculiar  and  various  qualities  in  the  bodies  which  we 
consider,  (namely,  the  heavenly  bodies,)  and  we  find  in 
the  end  that  all  these  qualities  resolve  themselves  into 
one  common  mechanical  property,  which  exists  alike  in 
all  bodies  and  parts  of  bodies.  On  the  contrary,  in 
studying  magnetical  and  electrical  laws,  we  appear  at  first 
to  have  a  single  extensive  phenomenon,  attraction  and 
repulsion :  but  in  our  attempts  to  generalize  this  pheno- 
menon, we  find  that  it  is  governed  by  conditions  depend- 
ing upon  something  quite  separate  from  the  bodies  them- 
selves, upon  the  presence  and  distribution  of  peculiar  and 
transitory  agencies ;  and,  so  far  as  we  can  discover,  the 
general  laws  of  these  agencies  are  of  a  chemical  nature, 
and  are  brought  into  action  by  peculiar  properties  of 
special  substances.  In  cosmical  phenomena,  everything,  in 
proportion  as  it  is  referred  to  mechanical  principles,  tends 
to  simplicity, — to  permanent  uniform  forces, —  to  one 
common,  positive,  property.  In  magnetical  and  electrical 
appearances,  on  the  contrary,  the  application  of  mecha- 
nical principles  leads  only  to  a  new  complexity,  which 
requires  a  new  explanation  ;  and  this  explanation  involves 
changeable  and  various  forces, — gradations  and  opposi- 
tions of  qualities.  The  doctrine  of  the  universal  gravita- 
tion of  matter  is  a  simple  and  ultimate  truth,  in  which 
the  mind  can  acquiesce  and  repose.  We  rank  gravity 
among  the  mechanical  attributes  of  matter,  and  we  see 
no  necessity  to  derive  it  from  any  ulterior  properties. 
Gravity  belongs  to  matter,  independent  of  any  conditions. 
But  the  conditions  of  magnetic  or  electrical  activity 
require  investigation  as  much  as  the  laws  of  their 
action.  Of  these  conditions  no  mere  mechanical  expla- 
pation  can  be  given ;  we  are  compelled  to  take 


DIFFUSION  OF  CLEAR  MECHANICAL  IDEAS.  265 

with  us  chemical  properties  and  relations  also  :  arid  thus 
magnetism,  electricity,  galvanism,  are  mechanico-chemical 
sciences. 

12.  Before  considering  these,  therefore,  I  shall  treat 
of  what  I  shall  call  Secondary  Mechanical  Sciences ;  by 
which  expression  I  mean  the  sciences  depending  upon 
certain  qualities  which  our  senses  discover  to  us  in  bodies ; 
Optics,  which  has  visible  phenomena  for  its  subject ; 
Acoustics,  the  science  of  hearing;  the  doctrine  of  Heat, 
a  quality  which  our  touch  recognises ;  to  this  last  science 
I  shall  take  the  liberty  of  sometimes  giving  the  name 
Thermotics,  analogous  to  the  names  of  the  other  two. 
If  our  knowledge  of  the  phenomena  of  Smell  and  Taste 
had  been  successfully  cultivated  and  systematized,  the 
present  part  of  our  work  would  be  the  place  for  the  phi- 
losophical discussion  of  those  sensations  as  the  subjects 
of  science. 

The  branches  of  knowledge  thus  grouped  in  one  class 
involve  common  Fundamental  Ideas,  from  which  their 
principles  are  derived  in  a  mode  analogous,  at  least  in  a 
certain  degree,  to  the  mode  in  which  the  principles  of 
the  mechanical  sciences  are  derived  from  the  fundamental 
ideas  of  causation  and  reaction.  We  proceed  now  to 
consider  these  Fundamental  Ideas,  their  nature,  develop- 
ment, and  consequences. 


266 


BOOK  IV. 


THE  PHILOSOPHY  OF    THE  SECONDARY 
MECHANICAL  SCIENCES. 


CHAPTER  I. 

OF  THE  IDEA  OF  A  MEDIUM  AS  COMMONLY 
EMPLOYED. 

1.  Of  Primary  and  Secondary  Qualities. — In  the  same 
way  in  which  the  mechanical  sciences  depend  upon  the 
Idea  of  Cause,  and  have  their  principles  regulated  by 
the  development  of  that  Idea,  it  will  be  found  that  the 
sciences  which  have  for  their  subject  Sound,  Light,  and 
Heat,  depend  for  their  principles  upon  the  Fundamental 
Idea  of  Media  by  means  of  which  we  perceive  those 
qualities.  Like  the  idea  of  cause,  this  idea  of  a  medium 
is  unavoidably  employed,  more  or  less  distinctly,  in  the 
common,  unscientific  operations  of  the  understanding ; 
and  is  recognised  as  an  express  principle  in  the  earliest 
speculative  essays  of  man.  But  here  also,  as  in  the  case 
of  the  mechanical  sciences,  the  developement  of  the  idea, 
and  the  establishment  of  the  scientific  truths  which 
depend  upon  it,  was  the  business  of  a  succeeding  period, 
and  was  only  executed  by  means  of  long  and  laborious 
researches,  conducted  with  a  constant  reference  to  experi- 
ment and  observation. 

Among  the  most  prominent  manifestations  of  the 
influence  of  the  idea  of  a  medium  of  which  we  have  now 
to  speak,  is  the  distinction  of  the  qualities  into  primary, 


OF  THE  IDEA  OF  A  MEDIUM.  267 

and  secondary  qualities.  This  distinction  has  been  con- 
stantly spoken  of  in  modern  times :  yet  it  has  often  been 
a  subject  of  discussion  among  metaphysicians  whether 
there  be  really  such  a  distinction,  and  what  the  true 
difference  is.  Locke  states  it  thus*:  original  or  primary 
qualities  of  body  are  "  such  as  are  utterly  inseparable 
from  the  body  in  what  estate  soever  it  may  be, — such  as 
sense  constantly  finds  in  every  particle  of  matter  which 
has  bulk  enough  to  be  perceived,  and  the  mind  finds 
inseparable  from  every  particle  of  matter,  though  less 
than  to  make  itself  singly  perceived  by  our  senses:"  and 
he  enumerates  them  as  solidity,  extension,  figure,  motion 
or  rest,  and  number.  Secondary  qualities,  on  the  other 
hand,  are  such  "  which  in  truth  are  nothing  in  the  objects 
themselves,  but  powers  to  produce  various  sensations  in 
us  by  their  primary  qualities,  i.  e.9  by  the  bulk,  figure, 
texture,  and  motion  of  their  insensible  parts,  as  colours, 
sounds,  tastes,  &c." 

Dr.  Reidf,  reconsidering  this  subject,  puts  the  differ- 
ence in  another  way.  There  is,  he  says,  a  real  foundation 
for  the  distinction  of  primary  and  secondary  qualities,  and 
it  is  this  :  "  That  our  senses  give  us  a  direct  and  distinct 
notion  of  the  primary  qualities,  and  inform  us  what  they 
are  in  themselves ;  but  of  the  secondary  qualities,  our 
senses  give  us  only  a  relative  and  obscure  notion.  They 
inform  us  only  that  they  are  qualities  that  affect  us  in  a 
certain  manner,  that  is,  produce  in  us  a  certain  sensation  ; 
but  as  to  what  they  are  in  themselves,  our  senses  leave  us 
in  the  dark." 

Dr.  Brown  ^  states  the  distinction  somewhat  other- 
wise. We  give  the  name  of  matter,  he  observes,  to  that 
which  has  extension  and  resistance :  these,  therefore,  are 
primary  qualities  of  matter,  because  they  compose  our 

*   Essay,  b.  ii.,  ch.  8.,  s.  9,  10.  t  Essays,  b.  ii.,  c.  1 7- 

f  Lectures,  ii.,  ]2. 


268      PHILOSOPHY  OF  SECONDARY  MECHANICAL  SCIENCES. 

definition  of  it.  All  other  qualities  are  secondary,  since 
they  are  ascribed  to  bodies  only  because  we  find  them 
associated  with  the  primary  qualities  which  form  our 
notion  of  those  bodies. 

It  is  not  necessary  to  criticise  very  strictly  these  vari- 
ous distinctions.  If  it  were,  it  would  be  easy  to  cavil  at 
them.  Thus  Locke,  it  may  be  observed,  does  not  point 
out  any  reason  for  believing  that  his  secondary  qualities 
are  produced  by  the  primary.  How  are  we  to  learn  that 
the  colour  of  a  rose  arises  from  the  bulk,  figure,  texture, 
and  motion  of  its  particles  ?  Certainly  our  senses  do  not 
teach  us  this ;  and  in  what  other  way,  on  Locke's  prin- 
ciples, can  we  learn  it?  Reid's  statement  is  not  more 
free  from  the  same  objection.  How  does  it  appear  that 
our  notion  of  warmth  is  relative  to  our  own  sensations 
more  than  our  notion  of  solidity?  And  if  we  take 
Brown's  account,  we  may  still  ask  whether  our  selection 
of  certain  qualities  to  form  our  idea  and  definition  of 
matter  be  arbitrary  and  without  reason  ?  If  it  be,  how 
can  it  make  a  real  distinction ;  if  it  be  not,  what  is  the 
reason  ? 

I  do  not  press  these  objections,  because  I  believe  that 
any  of  the  above  accounts  of  the  distinction  of  primary 
and  secondary  qualities  is  right  in  the  main,  however  im- 
perfect it  may  be.  The  difference  between  such  qualities 
as  extension  and  solidity  on  the  one  hand,  and  colour  or 
fragrance  on  the  other,  is  assented  to  by  all,  with  a  con- 
viction so  firm  and  indestructible^  that  there  must  be 
some  fundamental  principle  at  the  bottom  of  the  belief 
however  difficult  it  may  be  to  clothe  the  principle  in 
words.  That  successive  efforts  to  express  the  real  nature 
of  the  difference  were  made  by  men  so  clear-sighted  and 
acute  as  those  whom  I  have  quoted,  even  if  none  of  them 
are  satisfactory,  shows  how  strong  and  how  deeply-seated 
is  the  perception  of  truth  which  impels  us  to  suclj 
Attempts, 


OF    THE    IDEA    OF    A    MEDIUM.  269 

The  most  obvious  mode  of  stating  the  difference  of 
primary  and  secondary  qualities,  as  it  naturally  offers  itself 
to  speculative  minds,  appears  to  be  that  employed  by 
Locke,  slightly  modified.  Certain  of  the  qualities  of 
bodies,  as  their  bulk,  figure,  and  motion,  are  perceived 
immediately  in  the  bodies  themselves.  Certain  other 
qualities  as  sound,  colour,  heat,  are  perceived  by  means 
of  some  medium.  Our  conviction  that  this  is  the  case 
is  spontaneous  and  irresistible;  and  this  difference  of 
qualities  immediately  and  mediately  perceived  is  the  dis- 
tinction of  primary  and  secondary  qualities.  We  proceed 
further  to  examine  this  conviction. 

2.  The  Idea  of  Externality. — In  reasoning  concerning 
the  secondary  qualities  of  bodies,  we  are  led  to  assume 
the  bodies  to  be  external  to  us,  and  to  be  perceived  by 
means  of  some  medium  intermediate  between  us  and 
them.  These  assumptions  are  fundamental  conditions  of 
perception,  inseparable  from  it  even  in  thought. 

That  objects  are  external  to  us,  that  they  are  without 
us,  that  they  have  outness,  is  as  clear  as  it  is  that  these 
words  have  any  meaning  at  all.  This  conviction  is,  in- 
deed, involved  in  the  exercise  of  that  faculty  by  which 
we  perceive  all  things  as  existing  in  space ;  for  by  this 
faculty  we  place  ourselves  and  other  objects  in  one  com- 
mon space,  and  thus  they  are  exterior  to  us.  It  may  be 
remarked  that  this  apprehension  of  objects  as  external  to 
us,  although  it  assumes  the  idea  of  space,  is  far  from 
being  implied  in  the  idea  of  space.  The  objects  which 
we  contemplate  are  considered  as  existing  in  space,  and 
by  that  means  become  invested  with  certain  mutual  rela- 
tions of  position ;  but  when  we  consider  them  as  existing 
without  us,  we  make  the  additional  step  of  supposing 
ourselves  and  the  objects  to  exist  in  one  common  space. 
The  question  respecting  the  Ideal  Theory  of  Berkeley  has 
been  mixed  up  with  the  recognition  of  this  condition  of 


270      PHILOSOPHY  OF  SECONDARY  MECHANICAL  SCIENCES. 

the  externality  of  objects.  That  philosopher  maintained, 
as  is  well  known,  that  the  perceptible  qualities  of  bodies 
have  no  existence  except  in  a  perceiving  mind.  This 
system  has  often  been  understood  as  if  he  had  imagined 
the  world  to  be  a  kind  of  optical  illusion,  like  the  images 
which  we  see  when  we  shut  our  eyes,  appearing  to  be 
without  us,  though  they  are  only  in  our  organs  ;  and  thus 
this  Ideal  System  has  been  opposed  to  a  belief  in  an 
external  world.  In  truth,  however,  no  such  opposition 
exists.  The  Ideal  System  is  an  attempt  to  explain  the 
mental  process  of  perception,  and  to  get  over  the  diffi- 
culty of  mind  being  affected  by  matter.  But  the  author 
of  that  system  did  not  deny  that  objects  were  perceived 
under  the  conditions  of  space  and  mechanical  causation ; 
that  they  were  external  and  material  so  far  as  those 
words  describe  perceptible  qualities.  Berkeley's  system, 
however  visionary  or  erroneous,  did  not  prevent  his  enter- 
taining views  as  just,  concerning  optics  or  acoustics,  as  if 
he  had  held  any  other  doctrine  of  the  nature  of  perception. 

But  when  Berkeley's  theory  was  understood  as  a 
denial  of  the  existence  of  objects  without  us,  how  was  it 
answered  ?  If  we  examine  the  answers  which  are  given 
by  Reid  and  other  philosophers  to  this  hypothesis,  it  will 
be  found  that  they  amount  to  this :  that  objects  are  with- 
out us,  since  we  perceive  that  they  are  so ;  that  we  per- 
ceive them  to  be  external,  by  the  same  act  by  which  we 
perceive  them  to  be  objects.  And  thus,  in  this  stage  of 
philosophical  inquiry,  the  externality  of  objects  is  recog- 
nised as  one  of  the  inevitable  conditions  of  our  percep- 
tion of  them;  and  hence  the  idea  of  externality  is 
adopted  as  one  of  the  necessary  foundations  of  all  reason- 
ing concerning  all  objects  whatever. 

3.  Sensation  ly  a  Medium. — Objects,  as  we  have  just 
seen,  are  necessarily  apprehended  as  without  us ;  and  in 
general,  as  removed  from  us  by  a  great  or  small  distance. 


OF  THE  IDEA  OF  A  MEDIUM.  271 

Yet  they  affect  our  bodily  senses ;  and  this  leads  us  irre- 
sistibly to  the  conviction  that  they  are  perceived  by  means 
of  something  intermediate.  Vision,  or  hearing,  or  smell, 
or  the  warmth  of  a  fire,  must  be  communicated  to  us  by 
some  medium  of  sensation.  This  unavoidable  belief 
appears  in  all  attempts,  the  earliest  and  the  latest  alike, 
to  speculate  upon  such  subjects.  Thus,  for  instance, 
Aristotle  says*,  "Seeing  takes  place  in  virtue  of  some 
action  which  the  sentient  organ  suffers :  now  it  cannot 
suffer  action  from  the  colour  of  the  object  directly :  the 
only  remaining  possible  case  then  is,  that  it  is  acted  upon 
by  an  intervening  Medium ;  there  must  then  be  an  inter- 
vening Medium."  "  And  the  same  may  be  said,"  he  adds, 
"  concerning  sounding  and  odorous  bodies ;  for  these  do 
not  produce  sensation  by  touching  the  sentient  organ, 
but  the  intervening  Medium  is  acted  on  by  the  sound  or 
the  smell,  and  the  proper  organ,  by  the  Medium.... In 
sound  the  Medium  is  air ;  in  smell  we  have  no  name  for 
it."  In  the  sense  of  taste,  the  necessity  of  a  Medium 
is  not  at  first  so  obviously  seen,  because  the  object  tasted 
is  brought  into  contact  with  the  organ ;  but  a  little  atten- 
tion convinces  us  that  the  taste  of  a  solid  body  can  only 
be  perceived  when  it  is  conveyed  in  some  liquid  vehicle. 
Till  the  fruit  is  crushed,  and  till  its  juices  are  pressed  out, 
we  do  not  distinguish  its  flavour.  In  the  case  of  heat,  it 
is  still  more  clear  that  we  are  compelled  to  suppose  some 
invisible  fluid,  or  other  means  of  communication,  between 
the  distant  body  which  warms  us  and  ourselves. 

It  may  appear  to  some  persons  that  the  assumption 
of  an  intermedium  between  the  object  perceived  and  the 
sentient  organ  results  from  the  principles  which  form  the 
basis  of  our  mechanical  reasonings, — that  every  change 
must  have  a  cause,  and  that  bodies  can  act  upon  each 
other  only  by  contact.  It  cannot  be  denied  that  this 

II.  7. 


272     PHILOSOPHY  OF  SECONDARY  MECHANICAL  SCIENCES. 

principle  does  offer  itself  very  naturally  as  the  ground  of 
our  belief  in  media  of  sensation ;  and  it  appears  to  be 
referred  to  for  this  purpose  by  Aristotle  in  the  passage 
quoted  above.  But  yet  we  cannot  but  ask,  Does  the 
principle,  that  matter  produces  its  effect  by  contact  only, 
manifestly  apply  here?  When  we  so  apply  it,  we  include 
sensation  among  the  effects  which  material  contact  pro- 
duces ; — a  case  so  different  from  any  merely  mechanical 
effect,  that  the  principle,  so  employed,  appears  to  acquire 
a  new  signification.  May  we  not,  then,  rather  say  that 
we  have  here  a  new  axiom,  That  sensation  implies  a 
material  cause  immediately  acting  on  the  organ ;  than  a 
new  application  of  our  former  proposition,  That  all 
mechanical  change  implies  contact  ? 

The  solution  of  this  doubt  is  not  of  any  material  con- 
sequence to  our  reasonings ;  for  whatever  be  the  ground 
of  the  assumption,  it  is  certain  that  we  do  assume  the 
existence  of  media  by  which  the  sensations  of  sight, 
hearing,  and  the  like,  are  produced ;  and  it  will  be  seen 
shortly  that  principles  inseparably  connected  with  this 
assumption  are  the  basis  of  the  sciences  now  before  us. 

This  assumption  makes  its  appearance  in  the  physical 
doctrines  of  all  the  schools  of  philosophy.  It  is  exhibited 
perhaps  most  prominently  in  the  tenets  of  the  Epicureans, 
who  were  materialists,  and  extended  to  all  kinds  of  causa- 
tion the  axiom  of  the  existence  of  a  corporeal  mechanism 
by  which  alone  the  effect  is  produced.  Thus,  according  to 
them,  vision  is  produced  by  certain  images  or  material 
films  which  flow  from  the  object,  strike  upon  the  eyes, 
and  so  become  sensible.  This  opinion  is  urged  with 
great  detail  and  earnestness  by  Lucretius,  the  poetical 
expositor  of  the  Epicurean  creed  among  the  Romans. 
His  fundamental  conviction  of  the  necessity  of  a  material 
medium  is  obviously  the  basis  of  his  reasoning,  though  he 
attempts  to  show  the  existence  of  such  a  medium  by  facts. 


OF  THE  IDEA  OF  A  MEDIUM.  273 

Thus  he  argues*,  that  by  shouting  loud  we  make  the 
throat  sore ;  which  shows,  he  says,  that  the  voice  must  be 
material,  so  that  it  can  hurt  the  passage  in  coming  out. 

Hand  igitur  dubium  est  quin  voces  verbaque  constent 
Corporeis  e  principiis  ut  kedere  possint. 

4.  The  Process  of  Perception  of  Secondary  Qualities. 
— The  likenesses  or  representatives  of  objects  by  which 
they  affect  our  senses  were  called  by  some  writers  species, 
or  sensible  species,  a  term  which  continued  in  use  till 
the  revival  of  science.  It  may  be  observed  that  the 
conception  of  these  species  as  films  cast  off  from  the 
object,  and  retaining  its  shape,  was  different,  as  we  have 
seen,  from  the  view  which  Aristotle  took,  though  it  has 
sometimes  been  called  the  Peripatetic  doctrine  f.  We  may 
add  that  the  expression  was  latterly  applied  to  express 
the  supposition  of  an  emanation  of  any  kind,  and  implied 
little  more  than  that  supposition  of  a  medium  of  which 
we  are  now  speaking.  Thus  Bacon,  after  reviewing  the 
phenomena  of  sound,  sayst,  "  Videntur  motus  soni  fieri 
per  species  spirituales :  ita  enim  loquendum  donee  certius 
quippiam  inveniatur." 

Though  the  fundamental  principles  of  several  sciences 
depend  upon  the  assumption  of  a  medium  of  perception, 
these  principles  do  not  at  all  depend  upon  any  special 
view  of  the  process  of  our  perceptions.  The  mechanism 
of  that  process  is  a  curious  subject  of  consideration ;  but  it 
belongs  to  physiology,  more  properly  than  either  to  meta- 
physics, or  to  those  branches  of  physics  of  which  we  are 
now  speaking.  The  general  nature  of  the  process  is  the 
same  for  all  the  senses.  The  object  affects  the  appropriate 
intermedium;  the  medium,  through  the  proper  organ, 
the  eye,  the  ear,  the  nose,  affects  the  nerves  of  the  par- 

"  Lib.  iv.  529.  t  BROWN,  vol.  ii.,  p.  98. 

:£  Hist.  Son.  et  Aud.,  vol.  ix.,  p.  87. 
VOL.   I.  T 


274     PHILOSOPHY  OF  SECONDARY  MECHANICAL  SCIENCES. 

ticular  sense ;  and,  by  these,  in  some  way,  the  sensation 
is  conveyed  to  the  mind.  But  to  treat  the  impression 
upon  the  nerves  as  the  act  of  sensation  which  we  have  to 
consider,  would  be  to  mistake  our  object,  which  is  not  the 
constitution  of  the  human  body,  but  of  the  human  mind. 
It  would  be  to  mistake  one  link  for  the  power  which 
holds  the  end  of  the  chain.  No  anatomical  analysis  of 
the  corporeal  conditions  of  vision,  or  hearing,  or  feeling 
warm,  is  necessary  to  the  sciences  of  Optics,  or  Acoustics, 
or  Thermotics. 

Not  only  is  this  physiological  research  an  extraneous 
part  of  our  subject,  but  a  partial  pursuit  of  such  a  research 
may  mislead  the  inquirer.  We  perceive  objects  by  means 
of  certain  media,  and  by  means  of  certain  impressions  on 
the  nerves :  but  we  cannot  with  propriety  say  that  we 
perceive  either  the  media  or  the  impressions  on  the 
nerves.  What  person  in  the  act  of  seeing  is  conscious 
of  the  little  coloured  spaces  on  the  retina?  or  of  the 
motions  of  the  bones  of  the  auditory  apparatus  whilst  he 
is  hearing?  Surely,  no  one.  This  may  appear  obvious 
enough,  and  yet  a  writer  of  no  common  acuteness,  Dr. 
Brown,  has  put  forth  several  very  strange  opinions,  all 
resting  upon  the  doctrine  that  the  coloured  spaces  on  the 
retina  are  the  objects  which  we  perceive ;  and  there  are 
some  supposed  difficulties  and  paradoxes  on  the  same 
subject  which  have  become  quite  celebrated  (as  upright 
vision  with  inverted  images),  arising  from  the  same  con- 
fusion of  thought. 

As  the  consideration  of  the  difficulties  which  have 
arisen  respecting  the  philosophy  of  perception  may  serve 
still  further  to  illustrate  the  principles  on  which  we 
necessarily  reason  respecting  the  secondary  qualities  of 
bodies,  I  shall  here  devote  a  few  pages  to  that  subject. 


275 


CHAPTER  II. 

ON  PECULIARITIES  IN  THE  PERCEPTIONS  OP 
THE  DIFFERENT  SENSES. 

1.  WE  cannot  doubt  that  we  perceive  all  secondary 
qualities    by  means   of  immediate    impressions    made, 
through    the    proper   medium   of    sensation,   upon   our 
organs.     Hence  all   the   senses  are  sometimes  vaguely 
spoken  of  as  modifications  of  the  sense  of  feeling.     It 
will,  however,  be  seen,  on  reflection,  that  this  mode  of 
speaking  identifies  in  words  things  which  in  our  concep- 
tions have  nothing  in  common.     No  impression  on  the 
organs  of  touch  can  be  conceived  as  having  any  resem- 
blance to  colour  or  smell.     No  effort,  no  ingenuity,  can 
enable  us  to  describe  the  impressions  of  one  sense  in 
terms  borrowed  from  another. 

The  senses  have,  however,  each  its  peculiar  powers, 
and  these  powers  may  be  in  some  respects  compared,  so 
as  to  show  their  leading  resemblances  and  differences, 
and  the  characteristic  privileges  and  laws  of  each.  This 
is  what  we  shall  do  as  briefly  as  possible. 

(I.)  Prerogatives  of  Sight — The  sight  distinguishes 
colours,  as  the  hearing  distinguishes  tones;  the  sight 
estimates  degrees  of  brightness,  the  ear,  degrees  of  loud- 
ness  ;  but  with  several  resemblances,  there  are  most 
remarkable  differences  between  these  two  senses. 

2.  Position. — The  sight  has  this  peculiar  prerogative, 
that  it  apprehends  the  place  of  its  objects  directly  and 
primarily.      We  see  where  an   object   is   at   the   same 
instant  that  we  see  what  it  is.    If  we  see  two  objects,  we 
see  their  relative  position.     We  cannot  help  perceiving 
that  one  is  above  or  below,  to  the  right  or  to  the  left  of 
the  other,  if  we  perceive  them  at  all. 

T  2 


276      PHILOSOPHY  OF  SECONDARY  MECHANICAL  SCIENCES. 

There  is  nothing  corresponding  to  this  in  sound. 
When  we  hear  a  noise,  we  do  not  necessarily  assign  a 
place  to  it.  It  may  easily  happen  that  we  cannot  tell 
from  which  side  a  thnnder-clap  comes.  And  though  we 
often  can  judge  in  what  direction  a  voice  is  heard,  this  is  a 
matter  of  secondary  impression,  and  of  inference  from  con- 
comitant circumstances,  not  a  primary  fact  of  sensation. 
The  judgments  which  we  form  concerning  the  position  of 
sounding  bodies  are  obtained  by  the  conscious  or  uncon- 
scious comparison  of  the  impressions  made  on  the  two  ears, 
and  on  the  bones  of  the  head  in  general ;  they  are  not 
inseparable  conditions  of  hearing.  We  may  hear  sounds, 
and  be  uncertain  whether  they  are  "  above,  around,  or 
imderneath ;"  but  the  moment  any  thing  visible  appears, 
however  unexpected,  we  can  say  "  see  where  it  comes !" 

Since  we  can  see  the  relative  position  of  things,  we 
can  see  figure,  which  is  but  the  relative  position  of  the 
different  parts  of  the  boundary  of  the  object.  And  thus 
the  whole  visible  world  exhibits  to  us  a  scene  of  various 
shapes,  coloured  and  shaded  according  to  their  form  and 
position,  but  each  having  relations  of  position  to  all  the 
rest;  and  altogether,  entirely  filling  up  the  whole  range 
which  the  eye  can  command. 

3.  Distance. — The  distance  of  objects  from  us  is  no 
matter  of  immediate  perception,  but  is  a  judgment  and 
inference  formed  from  our  sensations,  in  the  same  way  as 
our  judgment  of  position  by  the  ear.  That  this  is  so, 
was  most  distinctly  shown  by  Berkeley,  in  his  New  Theory 
of  Vision.  The  elements  on  which  we  form  our  judgment 
are,  the  effort  by  which  we  fix  both  eyes  on  the  same 
object,  the  effort  by  which  we  adjust  each  eye  to  distinct 
vision,  and  the  known  forms,  colours,  and  parts  of  objects, 
as  compared  with  their  appearance.  The  right  interpre- 
tation of  the  information  which  these  circumstances  give 
us  respecting  the  true  distances  and  forms  of  things,  is 


PECULIARITIES  OF  THE  PERCEPTIONS.  277 

gradually  learned  by  experience,  the  lesson  being  begun 
in  our  earliest  infancy,  and  inculcated  upon  us  every  hour 
during  which  we  use  our  eyes.  The  completeness  with 
which  the  lesson  is  learned  is  truly  admirable ;  for  we  for- 
get that  our  conclusion  is  obtained  indirectly,  and  mistake 
a  judgment  on  evidence  for  an  intuitive  perception.  This, 
however,  is  not  more  surprising  than  the  rapidity  and 
unconsciousness  of  effort  with  which  we  understand  the 
meaning  of  the  speech  that  we  hear,  or  the  book  that  we 
read.  In  both  cases,  the  habit  of  interpretation  is  become 
as  familiar  as  the  act  of  perception.  And  this  is  the  case 
with  regard  to  vision.  We  see  the  breadth  of  the  street 
as  clearly  and  readily  as  we  see  the.  house  on  the  other 
side  of  it.  We  see  the  house  to  be  square,  however 
obliquely  it  be  presented  to  us.  Indeed  the  difficulty  is, 
to  recover  the  consciousness  of  our  real  and  original 
sensations ; — to  discover  what  is  the  apparent  relation  of 
the  lines  which  appear  before  us.  As  we  have  already 
said,  in  the  common  process  of  vision  we  suppose  our- 
selves to  see  that  which  cannot  be  seen ;  and  when  we 
would  make  a  picture  of  an  object,  the  difficulty  is  to 
represent  what  is  visible  and  no  more. 

But  perfect  as  is  our  habit  of  interpreting  what  we 
perceive,  we  could  not  interpret  if  we  did  not  perceive. 
If  the  eye  did  not  apprehend  visible  position,  it  could  not 
infer  actual  position,  which  is  collected  as  a  consequence : 
if  we  did  not  see  apparent  figure,  we  could  not  form  any 
opinion  concerning  real  form.  The  perception  of  place, 
which  is  the  prerogative  of  the  eye,  is  the  basis  of  all  its 
other  superiority. 

The  precision  with  which  the  eye  can  judge  of  apparent 
position  is  remarkable.  If  we  had  before  us  two  stars  dis- 
tant from  each  other  by  one-twentieth  of  the  moon's  dia- 
meter, we  could  easily  decide  the  apparent  direction  of  the 
one  from  the  other,  as  above  or  below,  to  the  right  or  left. 


278      PHILOSOPHY  OF  SECONDARY  MECHANICAL  SCIENCES. 

Yet  eight  millions  of  stars  might  be  placed  in  the  visible 
hemisphere  of  the  sky  at  such  distances  from  each  other ; 
and  thus  the  eye  would  recognise  the  relative  position  in 
a  portion  of  its  range  not  greater  than  one  eight-mil- 
lionth of  the  whole.  Such  is  the  accuracy  of  the  sense 
of  vision  in  this  respect;  and,  indeed,  we  might  with 
truth  have  stated  it  much  higher.  Our  judgment  of  the 
position  of  distant  objects  in  a  landscape  depends  upon 
features  far  more  minute  than  the  magnitude  we  have 
here  stated. 

As  our  object  is  to  point  out  principally  the  differ- 
ences of  the  senses,  we  do  not  dwell  upon  the  delicacy 
with  which  we  distinguish  tints  and  shades,  but  proceed 
to  another  sense. 

(II.)  Prerogatives  of  Hearing. — The  sense  of  hear- 
ing has  two  remarkable  prerogatives ;  it  can  perceive  a 
definite  and  peculiar  relation  between  certain  tones,  and 
it  can  clearly  perceive  two  tones  together ;  in  both  these 
circumstances  it  is  distinguished  from  vision,  and  from 
the  other  senses. 

4.  Musical  Intervals.— We  perceive  that  two  tones 
have,  or  have  not,  certain  definite  relations  to  each  other, 
which  we  call  Concords :  one  sound  is  a  Fifth,  an  Octave, 
&c.,  above  the  other.  And  when  this  is  the  case,  our  per- 
ception of  the  relation  is  extremely  precise.  It  is  easy 
to  perceive  when  a  fifth  is  out  of  tune  by  one-twentieth 
of  a  tone ;  that  is,  by  one-seventieth  of  itself.  To  this 
there  is  nothing  analogous  in  vision.  Colours  have  cer- 
tain vague  relations  to  one  another;  they  look  well 
together,  by  contrast  or  by  resemblance ;  but  this  is  an 
indefinite,  and  in  most  cases  a  casual  and  variable  feeling 
The  relation  of  complementary  colours  to  one  another,  as 
of  red  to  green,  is  somewhat  more  definite ;  but  still  has 
nothing  of  the  exactness  and  peculiarity  which  belongs 
to  a  musical  concord.  In  the  case  of  the  two  sounds, 


PECULIARITIES  OF  THE  PERCEPTIONS.  279 

there  is  an  exact  point  at  which  the  relation  obtains; 
when  by  altering  one  note  we  pass  this  point,  the  concord 
does  not  gradually  fade  away,  but  instantly  becomes  a 
discord;  and  if  we  go  further  still,  we  obtain  another 
concord  of  quite  a  different  character. 

We  learn  from  the  theory  of  sound  that  concords 
occur  when  the  times  of  vibration  of  the  notes  have  exact 
simple  ratios;  an  octave  has  these  times  as  1  to  2;  a 
fifth,  as  2  to  3.  According  to  the  undulatory  theory  of 
light,  such  ratios  occur  in  colours,  yet  the  eye  is  not 
affected  by  them  in  any  peculiar  way.  The  times  of  the 
undulations  of  certain  red  and  violet  rays  are  as  2  to  3, 
but  we  do  not  perceive  any  peculiar  harmony  or  con- 
nexion between  those  colours. 

5.  Chords. — Again,  the  ear  has  this  prerogative,  that  it 
can  apprehend  two  notes  together,  yet  distinct.     If  two 
notes,  distant  by  a  fifth  from  each  other,  are  sounded  on 
two  wind  instruments,  both  they  and  their  musical  rela- 
tion are  clearly  perceived.     There  is  not  a  mixture,  but 
a  concord,  an  interval.     In  colours,  the  case  is  otherwise. 
If  blue  and  yellow  fall  on  the  same  spot,  they  form  green; 
the  colour  is  simple  to  the  eye;    it  can  no  more  be 
decomposed  by  the  vision  than  if  it  were  the  simple  green 
of  the  prismatic  spectrum :    it  is  impossible  for  us,  by 
sight,  to  tell  whether  it  is  so  or  not. 

These  are  very  remarkable  differences  of  the  two 
senses :  two  colours  can  be  compounded  into  an  appa- 
rently simple  one  ;  two  sounds  cannot :  colours  pass  into 
each  other  by  gradations  and  intermediate  tints;  sounds 
pass  from  one  concord  to  another  by  no  gradations :  the 
most  intolerable  discord  is  that  whkh  is  near  a  concord. 
We  shall  hereafter  see  how  these  differences  affect  the 
scales  of  sound  and  of  colour. 

6.  Rhythm. — We  might  remark,  that  as  we  see  objects 
in  space,  we  hear  sounds  in  time ;  and  that  we  thus  intro- 


280      PHILOSOPHY  OF  SECONDARY  MECHANICAL  SCIENCES. 

duce  an  arrangement  among  sounds  which  has  several 
analogies  with  the  arrangement  of  objects  in  space. 
But  the  conception  of  time  does  not  seem  to  be  pecu- 
liarly connected  with  the  sense  of  hearing ;  a  faculty  of 
apprehending  tone  and  time,  or  in  musical  phraseology 
tune  and  rhythm,  are  certainly  very  distinct.  I  shall  not, 
therefore,  here  dwell  upon  such  analogies. 

The  other  Senses  have  not  any  peculiar  prerogatives, 
at  least  none  which  bear  on  the  formation  of  science.  I 
may,  however,  notice,  in  the  feeling  of  heat,  this  circum- 
stance ;  that  it  presents  us  with  two  opposites,  heat  and 
cold,  which  graduate  into  each  other.  This  is  not  quite 
peculiar,  for  vision  also  exhibits  to  us  white  and  black, 
which  are  clearly  opposites,  and  which  pass  into  each 
other  by  the  shades  of  gray. 

7.  First  Paradox  of  Vision.  Upright  Vision. — All 
our  senses  appear  to  have  this  in  common;  —  That 
they  act  by  means  of  organs,  in  which  a  bundle  of  nerves 
receives  the  impression  of  the  appropriate  medium  of  the 
sense.  In  the  construction  of  these  organs  there  are 
great  differences  and  peculiarities,  corresponding,  in  part 
at  least,  to  the  differences  in  the  information  given. 
Moreover,  in  some  cases,  as  we  have  noted  in  the  case  of 
audible  position  and  visible  distance,  that  which  seems  to 
be  a  perception  is  really  a  judgment  founded  on  percep- 
tions of  which  we  are  not  directly  aware.  It  will  be 
seen,  therefore,  that  with  respect  to  the  peculiar  powers 
of  each  sense,  it  may  be  asked ; — whether  they  can  be 
explained  by  the  construction  of  the  peculiar  organ ; — 
whether  they  are  acquired  judgments  and  not  direct  per- 
ceptions ; — or  whether  they  are  inexplicable  in  either  of 
these  ways,  and  cannot,  at  present  at  least,  be  resolved 
into  anything  but  conditions  of  the  intellectual  act  of 
perception. 

Two  of  these  questions  with  regard  to  vision,  have 


PECULIARITIES  OF  THE  PERCEPTIONS.  281 

been  much  discussed  by  psychological  writers :  the  cause 
of  our  seeing  objects  upright  by  inverted  images  on  the 
retina ;  and  of  our  seeing  single  with  two  such  images. 

Physiologists  have  very  completely  explained  the 
exquisitely  beautiful  mechanism  of  the  eye,  considered 
as  analogous  to  an  optical  instrument ;  and  it  is  in- 
disputable that  by  means  of  certain  transparent  lenses 
and  humours,  an  inverted  image  of  the  objects  which  are 
looked  at  is  formed  upon  the  retina,  or  fine  net-work  of 
nerve,  with  which  the  back  of  the  eye  is  lined.  We 
cannot  doubt  that  the  impression  thus  produced  on  these 
nerves  is  essential  to  the  act  of  vision ;  and  so  far  as  we 
consider  the  nerves  themselves  to  feel  or  perceive  by 
contact,  we  may  say  that  they  perceive  this  image,  or  the 
affections  of  light  which  it  indicates.  But  we  cannot 
with  any  propriety  say  that  we  perceive,  or  that  our  mind 
perceives,  this  image ;  for  we  are  not  conscious  of  it,  and 
none  but  anatomists  are  aware  of  its  existence :  we 
perceive  by  means  of  it. 

A  difficulty  has  been  raised,  and  dwelt  upon  in  a 
most  unaccountable  manner,  arising  from  the  neglect  of 
this  obvious  distinction.  It  has  been  asked,  how  is  it 
that  we  see  an  object,  a  man  for  instance,  upright,  when 
the  immediate  object  of  our  sensation,  the  image  of  the 
man  on  our  retina,  is  inverted  ?  To  this  we  must  answer, 
that  we  see  him  upright  because  the  image  is  inverted; 
that  the  inverted  image  is  the  necessary  means  of  seeing 
an  upright  object.  This  is  granted,  and  where  then  is 
the  difficulty?  Perhaps  it  may  be  put  thus :  How  is  it 
that  we  do  not  judge  the  man  to  be  inverted,  since  the 
sensible  image  is  so?  To  this  we  may  reply,  that  we 
have  no  notion  of  upright  or  inverted,  except  that  which 
is  founded  on  experience,  and  that  all  our  experience, 
without  exception,  must  have  taught  us  that  such  a 
sensible  image  belongs  to  a  man  who  is  in  an  upright 


282      PHILOSOPHY  OF  SECONDARY  MECHANICAL  SCIENCES. 

position.  Indeed,  the  contrary  judgment  is  not  con- 
ceivable ;  a  man  is  upright  whose  head  is  upwards  and 
his  feet  downwards.  But  what  are  the  sensible  images 
of  upwards  and  downwards  f  Whatever  be  our  standard 
of  up  and  down,  the  sensible  representation  of  up  will  be 
an  image  moving  on  the  retina  towards  the  lower  side, 
and  the  sensible  representation  of  down  will  be  a  motion 
towards  the  upper  side.  The  head  of  the  man's  image  is 
towards  the  image  of  the  sky,  its  feet  are  towards  the 
image  of  the  ground ;  how  then  should  it  appear  other- 
wise than  upright?  But,  perhaps,  we  expect  that  the 
whole  world  should  appear  inverted;  but  if  the  whole 
be  inverted,  how  is  the  relation  of  the  parts  altered? 
or  we  expect  that  we  should  think  our  own  persons 
inverted:  yet  this  cannot  be,  for  we  look  at  them 
as  we  do  at  other  objects :  Or,  perhaps  we  expect 
that  things  should  appear  to  fall  upwards ;  yet  what  do 
we  know  of  upwards,  except  that  it  is  the  direction 
in  which  bodies  do  not  fall?  In  short,  the  whole 
of  this  difficulty,  though  it  has  in  no  small  degree  em- 
barrassed metaphysicians,  appears  to  result  from  a  very 
palpable  confusion  of  ideas;  from  an  attempt  at  com- 
parison of  what  we  see,  with  that  which  the  retina  feels, 
as  if  they  were  separately  presentable.  It  is  a  sufficient 
explanation  to  say,  that  we  do  not  see  the  image  on  the 
retina,  but  see  by  means  of  it.  The  perplexity  does  not 
require  much  more  skill  to  disentangle,  than  it  does  to 
see  that  a  word  written  in  black  ink,  may  signify  white. 

8.  Second  Paradox  of  Vision.  Single  Vision. — 
(1.)  Small  or  Distant  Objects. — The  other  difficulty,  why 
with  two  images  on  the  retina  we  see  only  one  object,  is 
of  a  much  more  real  and  important  kind.  This  effect  is 
manifestly  limited  by  certain  circumstances  of  a  very 
precise  nature ;  for  if  we  direct  our  eyes  at  an  object 
which  is  very  near  the  eye,  we  see  all  other  objects 


PECULIARITIES  OF  THE  PERCEPTIONS.  283 

double.  The  fact  is  not,  therefore,  that  we  are  incapable 
of  receiving  two  impressions  from  the  two  images,  but 
that,  under  certain  conditions,  the  two  impressions  form 
one.  A  little  attention  shows  us  that  these  conditions 
are,  that  with  both  eyes  we  should  look  at  the  same 
object ;  and  again,  we  find  that  to  look  at  an  object  with 
either  eye,  is  to  direct  the  eye  so  that  the  image  falls  on 
or  near  a  particular  point  about  the  middle  of  the  retina. 
Thus  these  middle  points  in  the  two  retinas  correspond, 
and  we  see  an  image  single  when  the  two  images  fall  on 
the  corresponding  points. 

Again,  as  each  eye  judges  of  position,  and  as  the  two 
eyes  judge  similarly,  an  object  will  be  seen  in  the  same 
place  by  one  eye  and  by  the  other,  when  the  two  images 
which  it  produces  are  similarly  situated  with  regard  to 
the  corresponding  points  of  the  retina. 

This  is  the  Law  of  Single  Vision,  at  least  so  far  as 
regards  small  objects  ;  namely,  objects  so  small  that  in  con- 
templating them  we  consider  their  position  only,  and  not 
their  solid  dimensions.  The  law  is  a  distinct  and  original 
principle  of  our  constitution ;  and  it  is  a  mistake  to  call  in, 
as  some  have  done,  the  influence  of  habit  and  of  acquired 
judgments,  in  order  to  determine  the  result  in  such  cases. 

To  ascribe  the  apparent  singleness  of  objects  to  the 
impressions  of  vision  corrected  by  the  experience  of 
touch*,  would  be  to  assert  that  a  person  who  had  not 
been  in  the  habit  of  handling  what  lie  saw,  would  see  all 
objects  double ;  and  also,  to  assert  that  a  person  begin- 
ning with  the  double  world  which  vision  thus  offers  to 
him,  would,  by  the  continued  habit  of  handling  objects, 
gradually  and  at  last  learn  to  see  them  single.  But  all 
the  facts  of  the  case  show  such  suppositions  to  be 
utterly  fantastical.  No  one  can,  in  this  case,  go  back 
from  the  habitual  judgment  of  the  singleness  of  objects, 

*  £ee  BROWN,  vol.  ii.  p.  81. 


284      PHILOSOPHY  OF  SECONDARY  MECHANICAL  SCIENCES. 

to  the  original  and  direct  perception  of  their  doubleness, 
as  the  draughtsman  goes  back  from  judgments  to  per- 
ception, in  representing  solid  distances  and  forms  by 
means  of  perspective  pictures.  No  one  can  point  out 
any  case  in  which  the  habit  is  imperfectly  formed ;  even 
children  of  the  most  tender  age  look  at  an  object  with 
both  eyes,  and  see  it  as  one. 

In  cases  when  the  eyes  are  distorted  (in  squinting), 
one  eye  only  is  used,  or  if  both  are  employed,  there  is 
double  vision ;  and  thus  any  derangement  of  the  corre- 
spondence of  motion  in  the  two  eyes  will  produce  double- 
sightedness. 

Brown  is  one  of  those*  who  assert  that  two  images 
suggest  a  single  object  because  we  have  always  found 
two  images  to  belong  to  a  single  object.  He  urges  as 
an  illustration,  that  the  two  words  "  he  conquered," 
by  custom  excite  exactly  the  same  notion  as  the  one 
Latin  word  "  vicit ;"  and  thus  that  two  visual  images, 
by  the  effect  of  habit,  produce  the  same  belief  of  a 
single  object  as  one  tactual  impression.  But  in  order 
to  make  this  pretended  illustration  of  any  value,  it  ought 
to  be  true  that  when  a  person  has  thoroughly  learnt 
the  Latin  language,  he  can  no  longer  distinguish  any 
separate  meaning  in  "  he"  and  in  "  conquered."  We  can 
by  no  effort  perceive  the  double  sensation,  when  we 
look  at  the  object  with  the  two  eyes.  Those  who  squint, 
learn  by  habit  to  see  objects  single  :  but  the  habit  which 
they  acquire  is  that  of  attending  to  the  impressions  of 
one  eye  only  at  once,  not  of  combining  the  two  impres- 
sions. It  is  obvious,  that  if  each  eye  spreads  before  us 
the  same  visible  scene,  with  the  same  objects  and  the 
same  relations  of  place,  then,  if  one  object  in  each  scene 
coincide,  the  whole  of  the  two  visible  impressions  will  be 
coincident.  And  here  the  remarkable  circumstance  is, 
*  Lectures^  vol.  ii.  p.  81. 


PECULIARITIES  OF  THE  PERCEPTIONS.  285 

that  not  only  each  eye  judges  for  itself  of  the  relations  of 
position  which  come  within  its  field  of  view ;  but  that 
there  is  a  superior  and  more  comprehensive  faculty 
which  combines  and  compares  the  two  fields  of  view  ; 
which  asserts  or  denies  their  coincidence ;  which  con- 
templates, as  in  a  relative  position  to  one  another,  these 
two  visible  worlds,  in  which  all  other  relative  position  is 
given.  This  power  of  confronting  two  sets  of  visible 
images  and  figured  spaces  before  a  purely  intellectual 
tribunal,  is  one  of  the  most  remarkable  circumstances  in 
the  sense  of  vision. 

9.  (2.)  Near  Objects. — We  have  hitherto  spoken  of  the 
singleness  of  objects  whose  images  occupy  corresponding 
positions  on  the  retina  of  the  two  eyes.  But  here  occurs 
a  difficulty.  If  an  object  of  moderate  size,  a  small  thick 
book  for  example,  be  held  at  a  little  distance  from  the 
eyes,  it  produces  an  image  on  the  retina  of  each  eye ;  and 
these  two  images  are  perspective  representations  of  the 
book  from  different  points  of  view,  (the  positions  of  the 
two  eyes,)  and  are  therefore  of  different  forms.  Hence 
the  two  images  cannot  occupy  corresponding  points  of 
the  retina  throughout  their  whole  extent.  If  the  central 
parts  of  the  two  images  occupy  corresponding  points,  the 
boundaries  of  the  two  will  not  correspond.  How  is  it 
then  consistent  with  the  law  above  stated,  that  in  this 
case  the  object  appears  single  ? 

It  may  be  observed,  that  the  two  images  in  such  a 
case  will  differ  most  widely  when  the  object  is  not  a 
mere  surface,  but  a  solid.  If  a  book,  for  example,  be 
held  with  one  of  its  edges  towards  the  face,  the  right  eye 
will  see  one  side  more  directly  than  the  left  eye,  and 
the  left  eye  will  see  another  side  more  directly,  and  the 
outline  of  the  two  images  upon  the  two  retinas  will  ex- 
hibit this  difference.  And  it  may  be  further  observed, 
that  this  difference  in  the  images  received  by  the  two 


286      PHILOSOPHY  OF  SECONDARY  MECHANICAL  SCIENCES. 

eyes,  is  a  plain  and  demonstrative  evidence  of  the  solidity 
of  the  object  seen;  since  nothing  but  a  solid  object 
could  (without  some  special  contrivance)  produce  these 
different  forms  of  the  images  in  the  two  eyes. 

Hence  the  absence  of  exact  coincidence  in  the  two 
images  on  the  retina  is  the  necessary  condition  of  the 
solidity  of  the  object  seen,  and  must  be  one  of  the  indi- 
cations by  means  of  which  our  vision  apprehends  an 
object  as  solid.  And  that  this  is  so,  Mr.  Wheatstone 
has  proved  experimentally,  by  means  of  some  most 
ingenious  and  striking  contrivances.  He  has  devised* 
an  instrument  by  which  two  images  (drawn  in  outline) 
differing  exactly  as  much  as  the  two  images  of  a  solid 
body  seen  near  the  face  would  differ,  are  conveyed, 
one  to  one  eye,  and  the  other  to  the  other.  And  it  is 
found  that  when  this  is  effected,  the  object  which  the 
images  represent  is  not  only  seen  single,  but  is  appre- 
hended as  solid  with  a  clearness  and  reality  of  conviction 
quite  distinct  from  any  impression  which  a  mere  per- 
spective representation  can  give. 

At  the  same  time  it  is  found  that  the  object  is  then 
only  apprehended  as  single  when  the  two  images  are 
such  as  are  capable  of  being  excited  by  one  single  object 
placed  in  solid  space,  and  seen  by  the  two  eyes.  If  the 
images  differ  more  or  otherwise  than  this  condition 
allows,  the  result  is,  that  both  are  seen,  their  lines  cross- 
ing and  interfering  with  one  another. 

It  may  be  observed,  too,  that  if  an  object  be  of  such 
large  size  as  not  to  be  taken  in  by  a  single  glance  of  the 
eyes,  it  is  no  longer  apprehended  as  single  by  a  direct  act 
of  perception ;  but  its  parts  are  looked  at  separately  and 
successively,  and  the  impressions  thus  obtained  are  put 
together  by  a  succeeding  act  of  the  mind.  Hence  the 
objects  which  are  directly  seen  as  solid,  will  be  of  mode- 

*  Phil.  Trans.,  1839. 


PECULIARITIES  OF  THE  PERCEPTIONS.  287 

rate  size ;  in  which  case  it  is  not  difficult  to  show  that 
the  outlines  of  the  two  images  will  differ  from  each  other 
only  slightly. 

Hence  we  are  led  to  the  following,  as  the  Law  of 
Single  Vision  for  near  objects  : — When  the  two  images 
in  the  two  eyes  are  situated  (part  for  part)  nearly,  but  not 
exactly,  upon  corresponding  points,  the  object  is  appre- 
hended as  single,  if  the  two  images  are  such  as  are  or  would 
be  given  by  a  single  solid  object  seen  by  the  two  eyes 
separately  :  and  in  this  case  the  object  is  necessarily 
apprehended  as  solid. 

This  law  of  vision  does  not  contradict  that  stated 
above  for  distant  objects :  for  when  an  object  is  removed 
to  a  considerable  distance,  the  images  in  the  two  eyes 
coincide  exactly,  and  the  object  is  seen  as  single,  though 
without  any  direct  apprehension  of  its  solidity.  The  first 
law  is  a  special  case  of  the  second.  Under  the  condition 
of  exactly  corresponding  points,  we  have  the  perception 
of  singleness,  but  no  evidence  of  solidity.  Under  the 
condition  of  nearly  corresponding  points,  we  may  have 
the  perception  of  singleness,  and  with  it,  of  solidity. 

We  have  before  noted  it  as  an  important  feature  in 
our  visual  perception,  that  while  we  have  two  distinct 
impressions  upon  the  sense,  which  we  can  contemplate 
separately  and  alternately,  (the  impressions  on  the  two 
eyes,)  we  have  a  higher  perceptive  faculty  which  can 
recognise  these  two  impressions,  exactly  similar  to  each 
other,  as  only  two  images  of  one  and  the  same  assemblage 
of  objects.  But  we  now  see  that  the  faculty  by  which 
we  perceive  visible  objects  can  do  much  more  than  this : 
—it  can  not  only  unite  two  impressions,  and  recognise 
them  as  belonging  to  one  object  in  virtue  of  their  coin- 
cidence, but  it  can  also  unite  and  identify  them,  even 
when  they  do  not  exactly  coincide.  It  can  correct  and 
adjust  their  small  difference,  so  that  they  are  both  appre- 


288     PHILOSOPHY  OF  SECONDARY  MECHANICAL  SCIENCES. 

hended  as  representations  of  the  same  figure.  It  can 
infer  from  them  a  real  form,  not  agreeing  with  either  of 
them ;  and  a  solid  space,  which  they  are  quite  incapable 
of  exemplifying.  The  visual  faculty  decides  whether  or 
not  the  two  ocular  images  can  be  pictures  of  the  same 
solid  object,  and  if  they  can,  it  undoubtingly  and  neces- 
sarily accepts  them  as  being  so.  This  faculty  operates  as 
if  it  had  the  power  of  calling  before  it  all  possible  solid 
figures,  and  of  ascertaining  by  trial  whether  any  of  those 
will,  at  the  same  time,  fit  both  the  outlines  which  are 
given  by  the  sense.  It  assumes  the  reality  of  solid  space, 
and,  if  it  be  possible,  reconciles  the  appearances  with  that 
reality.  And  thus  an  activity  of  the  mind  of  a  very 
remarkable  and  peculiar  kind  is  exercised  in  the  most 
common  act  of  seeing. 

10.  It  may  be  said  that  this  doctrine,  of  such  a  visual 
faculty  as  has  been  described,  is  very  vague  and  obscure, 
since  we  are  not  told  what  are  its  limits.  It  adjusts  and 
corrects  figures  which  nearly  coincide,  so  as  to  identify 
them.  But  how  nearly,  it  may  be  asked,  must  the  figures 
approach  each  other,  in  order  that  this  adjustment  may 
be  possible  ?  What  discrepance  renders  impossible  the 
reconcilement  of  which  we  .speak?  Is  it  not  impossible 
to  give  a  definite  answer  to  these  questions,  and  therefore 
impossible  to  lay  down  definitely  such  laws  of  vision  as 
we  have  stated  ?  To  this  I  reply,  that  the  indefiniteness 
thus  objected  to  us,  is  no  new  difficulty,  but  one  with 
which  philosophers  are  familiar,  and  to  which  they  are 
already  reconciled.  It  is,  in  fact,  no  other  than  the 
indefiniteness  of  the  limits  of  distinct  vision.  How  near 
to  the  face  must  an  object  be  brought,  so  that  we  shall 
cease  to  see  it  distinctly?  The  distance,  it  will  be 
answered,  is  indefinite :  it  is  different  for  different  per- 
sons ;  and  for  the  same  person,  it  varies  with  the  degree 
of  effort,  attention,  and  habit.  But  this  indefiniteness  is 


PECULIARITIES  OF  THE  PERCEPTIONS.  289 

only  the  indefiniteness,  in  another  form,  of  the  deviation 
of  the  two  ocular  images  from  one  another :  and  in  reply 
to  the  question  concerning  them  we  must  still  say,  as 
before,  that  in  doubtful  cases,  the  power  of  apprehending 
an  object  as  single,  when  this  can  be  done,  will  vary  with 
effort,  attention,  and  habit.  The  assumption  that  the 
apparent  object  exists  as  a  real  figure,  in  real  space,  is  to 
be  verified,  if  possible ;  but,  in  extreme  cases,  from  the 
unfitness  of  the  point  of  view,  or  from  any  other  cause  of 
visual  confusion  or  deception,  the  existence  of  a  real 
object  corresponding  to  the  appearance  may  be  doubtful ; 
as  in  any  other  kind  of  perception  it  may  be  doubtful 
whether  our  senses,  under  disadvantageous  circumstances, 
give  us  true  information.  The  vagueness  of  the  limits, 
then,  within  which  this  visual  faculty  can  be  successfully 
exercised,  is  no  valid  argument  against  the  existence  of 
the  faculty,  or  the  truth  of  the  law  which  we  have  stated 
concerning  its  action. 

11.  Visible  Figure.  —  There  is  one  tenet  on  the 
subject  of  vision  which  appears  to  me  so  extravagant 
and  unphilosophical,  that  I  should  not  have  thought  it 
necessary  to  notice  it,  if  it  bad  not  been  recently  pro- 
mulgated by  a  writer  of  great  acuteness  in  a  book  which 
has  obtained,  for  a  metaphysical  work,  considerable  cir- 
culation. I  speak  of  Brown's  opinion*  that  we  have  no 
immediate  perception  of  visible  figure.  I  confess  myself 
unable  to  comprehend  fully  the  doctrine  which  he  would 
substitute  in  the  place  of  the  one  commonly  received.  He 
states  it  thusf:  "When  the  simple  affection  of  sight  is 
blended  with  the  ideas  of  suggestion  [those  arising  from 
touch,  &c.]  in  what  are  termed  the  acquired  perceptions 
of  vision,  as,  for  example,  in  the  perception  of  a  sphere, 
it  is  colour  only  which  is  blended  with  the  large  con- 
vexity, and  not  a  small  coloured  plane."  The  doctrine 

*  Lectures,  vol.  ii.,  p.  82.  t  Ib.9  vol.  ii.,  p.  90. 

VOL,  I.  U 


290      PHILOSOPHY  OF  SECONDARY  MECHANICAL  SCIENCES. 

which  Brown  asserts  in  this  and  similar  passages,  appears 
to  be,  that  we  do  not  by  vision  perceive  both  colour  and 
figure ;  but  that  the  colour  which  we  see  is  blended  with 
the  figure  which  we  learn  the  existence  of  by  other 
means,  as  by  touch.  But  if  this  were  possible  when  we 
can  call  in  other  perceptions,  how  is  it  possible  when  we 
cannot  or  do  not  touch  the  object?  Why  does  the 
moon  appear  round,  gibbous,  or  horned  ?  What  sense 
besides  vision  suggests  to  us  the  idea  of  her  figure  ?  And 
even  in  objects  which  we  can  reach,  what  is  that  circum- 
stance in  the  sense  of  vision  which  suggests  to  us  that 
the  colour  belongs  to  the  sphere,  except  that  we  see  the 
colour  where  we  see  the  sphere  ?  If  we  do  not  see  figure, 
we  do  not  see  position ;  for  figure  is  the  relative  position 
of  the  parts  of  a  boundary.  If  we  do  not  see  position, 
why  do  we  ascribe  the  yellow  colour  to  the  sphere  on  our 
left,  rather  than  to  the  cube  on  our  right  ?  We  associate 
the  colour  with  the  object,  says  Dr.  Brown ;  but  if  his 
opinion  were  true,  we  could  not  associate  two  colours 
with  two  objects,  for  we  could  not  apprehend  the  colours 
as  occupying  two  different  places. 

The  whole  of  Brown's  reasoning  on  this  subject  is  so 
irreconcileable  with  the  first  facts  of  vision,  that  it  is 
difficult  to  conceive  how  it  could  proceed  from  a  person 
who  has  reasoned  with  great  acuteness  concerning  touch. 
In  order  to  prove  his  assertion,  he  undertakes  to  examine 
the  only  reasons  which,  he  says*,  he  can  imagine  for 
believing  the  immediate  perception  of  visible  figure :  (1) 
That  it  is  absolutely  impossible,  in  our  present  sensations 
of  sight,  to  separate  colour  from  extension ;  and  (2)  That 
there  are,  in  fact,  figures  on  the  retina  corresponding  to 
the  apparent  figures  of  objects. 

On  the  subject  of  the  first  reason,  he  says,  that  the 
figure  which  we  perceive  as  associated  with  colour,  is  the 
real,  and  not  the  apparent  figure.  "  Is  there,"  he  asks, 
*  Lectures,  vol.  ii.5  p.  83. 


\  PECULIARITIES  OF  THE  PERCEPTIONS.  201 

"the  slightest  consciousness  of  a  perception  of  visible 
figure,  corresponding  to  the  affected  portion  of  the 
retina  ?"  To  which,  though  he  seems  to  think  an  affirma- 
tive answer  impossible,  we  cannot  hesitate  to  reply,  that 
there  is  undoubtedly  such  a  consciousness ;  that  though 
obscured  by  being  made  the  ground  of  habitual  inference 
as  to  the  real  figure,  this  consciousness  is  constantly 
referred  to  by  the  draughtsmen,  and  easily  recalled  by 
any  one.  We  may  separate  colour,  he  says  again*, 
from  the  figures  on  the  retina,  as  we  may  separate  it  from 
length,  breadth,  and  thickness,  which  we  do  not  see.  But 
this  is  altogether  false :  we  cannot  separate  colour  from 
length,  breadth,  and  thickness  in  any  other  way>  than 
by  transferring  it  to  the  visible  figure  which  we  do 
see.  He  cannot,  he  allows,  separate  the  colour  from 
the  visible  form  of  the  trunk  of  a  large  oak  ;  but  just  as 
little,  he  thinks,  can  he  separate  it  from  the  convex  mass 
of  the  trunk,  which  (it  is  allowed  on  all  hands)  he  does  not 
immediately  see.  But  in  this  he  is  mistaken :  for  if  he 
were  to  make  a  picture  of  the  oak,  he  would  separate  the 
colour  from  the  convex  shape,  which  he  does  not  imitate, 
but  he  could  not  separate  it  from  the  visible  figure,  which 
he  does  imitate ;  and  he  would  then  perceive  that  the 
fact  that  he  has  not  an  immediate  perception  of  the  con- 
vex form,  is  necessarily  connected  with  the  fact  that  he 
has  an  immediate  perception  of  the  apparent  figure ;  so 
far  is  the  rejection  of  immediate  perception  in  the  former 
case  from  being  a  reason  for  rejecting  it  in  the  latter. 

Again,  with  regard  to  the  second  argument.  It  does 
not,  he  says,  follow,  that  because  a  certain  figured  portion 
of  the  retina  is  affected  by  light,  we  should  see  such  a 
figure ;  for  if  a  certain  figured  portion  of  the  olfactory 
organ  were  affected  by  odours,  we  should  not  acquire  by 
smell  any  perception  of  such  figuref .  This  is  merely  to 

*   Lectures,  vol.  ii.,  p.  84.  t  /&.,  p.  87. 


202      PHILOSOPHY  OF  SECONDARY  MECHANICAL  SCIENCES. 

say,  that  because  we  do  not  perceive  position  and  figure 
by  one  sense,  we  cannot  do  so  by  another.  But  this 
again  is  altogether  erroneous.  It  is  an  office  of  our 
sight  to  inform  us  of  position,  and  consequently  of  figure  ; 
for  this  purpose,  the  organ  is  so  constructed  that  the 
position  of  the  object  determines  the  position  of  the 
point  of  the  retina  affected.  There  is  nothing  of  this 
kind  in  the  organ  of  smell ;  objects  in  different  positions 
and  of  different  forms  do  not  affect  different  parts  of  the 
olfactory  nerve,  or  portions  of  different  shape.  Different 
objects,  remote  from  each  other,  if  perceived  by  smell, 
affect  the  same  part  of  the  olfactory  organs.  This  is  all 
quite  intelligible ;  for  it  is  not  the  office  of  smell  to 
inform  us  of  position.  Of  what  use  or  meaning  would 
be  the  curious  and  complex  structure  of  the  eye,  if  it 
gave  us  only  such  vague  and  wandering  notions  of  the 
colours  and  forms  of  the  flowers  in  a  garden,  as  we 
receive  from  their  odours  when  we  walk  among  them 
blindfold?  It  is,  as  we  have  said,  the  prerogative  of 
vision  to  apprehend  position :  the  places  of  objects  on 
the  retina  give  this  information.  We  do  not  suppose 
that  the  affection  of  a  certain  shape  of  nervous  expanse 
will  necessarily  and  in  all  cases  give  us  the  impression  of 
figure ;  but  we  know  that  in  vision  it  does ;  and  it  is 
clear  that  if  we  did  not  acquire  our  acquaintance  with 
visible  figure  in  this  way,  we  could  not  acquire  it  in 
any  way*. 

The  whole  of  this  strange  mistake  of  Brown's  appears 
to  arise  from  the  fault  '^already  noticed  ; — that  of  consi- 
dering the  image  on  the  retina  as  the  object  instead  of 

*  When  Brown  says  further  (p.  87,)  that  we  can  indeed  show  the 
image  in  the  dissected  eye ;  but  that  "it  is  not  in  the  dissected  eye 
that  vision  takes  place ;"  it  is  difficult  to  see  what  his  drift  is.  Does 
he  doubt  that  there  is  an  image  formed  in  the  living  as  completely  as 
in  the  dissected  eye  ? 


PECULIARITIES  OF  THE  PERCEPTIONS.  293 

the  means  of  vision.  This  indeed  is  what  he  says :  "  the 
true  object  of  vision  is  not  the  distant  body  itself,  but 
the  light  that  has  reached  the  expansive  termination  of 
the  optic  nerve*."  Even  if  this  were  so,  we  do  not  see 
why  we  should  not  perceive  the  position  of  the  impression 
on  this  expanded  nerve.  But  as  we  have  already  said* 
the  impression  on  the  nerve  is  the  means  of  vision,  and 
enables  us  to  assign  a  place,  or  at  least  a  direction,  to  the 
object  from  which  the  light  proceeds,  and  thus  makes 
vision  possible.  Brown,  indeed,  pursues  his  own  peculiar 
view  till  he  involves  the  subject  in  utter  confusion.  Thus 
he  saysf,  "According  to  the  common  theory  [that 
figure  can  be  perceived  by  the  eye,]  a  visible  sphere  is  at 
once  to  my  perception  convex  and  plane ;  and  if  the 
sphere  be  a  large  one,  it  is  perceived  at  once  to  be  a 
sphere  of  many  feet  in  diameter,  and  a  plane  circular 
surface  of  the  diameter  of  a  quarter  of  an  inch."  It  is 
easy  to  deduce  these  and  greater  absurdities,  if  we  pro- 
ceed on  his  strange  and  baseless  supposition  that  the 
object  and  the  image  on  the  retina  are  loth  perceived. 
But  who  is  conscious  of  the  image  on  the  retina  in  any 
other  way  than  as  he  sees  the  object  by  means  of  it  ? 

Brown  seems  to  have  imagined  that  he  was  ana- 
lysing the  perception  of  figure  in  the  same  manner  in 
which  Berkeley  had  analysed  the  perception  of  distance. 
He  ought  to  have  recollected  that  such  an  undertaking, 
to  be  successful,  required  him  to  show  what  elements  he 
analysed  it  into.  Berkeley  analysed  the  perception  of 
real  figure  into  the  interpretation  of  visible  figure  accord- 
ing to  certain  rules  which  he  distinctly  stated.-  Brown 
analyses  the  perception  of  visible  figure  into  no  elements. 
Berkeley  says,  that  we  do  not  directly  perceive  distance, 
but  that  we  perceive  something  else,  from  which  we  infer 
distance,  namely,  visible  figure  and  colour,  and  our  own. 

*  Lectures,  vol.  ii,  p.  57.  t  lb.t  vol.  ii.,  p»  89. 


294      PHILOSOPHY  OF  SECONDARY  MECHANICAL  SCIENCES. 

efforts  in  seeing ;  Brown  says,  that  we  do  not  see  figure, 
but  infer  it ;  what  then  do  we  see  which  we  infer  it  from? 
To  this  he  offers  no  answer.  He  asserts  the  seeming 
perception  of  visible  figure  to  be  a  result  of  "  associa- 
tion ;" — of  "  suggestion."  But  what  meaning  can  we 
attach  to  this?  Suggestion  requires  something  which 
suggests ;  and  not  a  hint  is  given  what  it  is  which  sug- 
gests position.  Association  implies  two  things  asso- 
ciated ;  what  is  the  sensation  which  we  associate  with 
form?  What  is  that  visual  perception  which  is  not 
figure,  and  which  we  mistake  for  figure  ?  What  percep- 
tion is  it  that  suggests  a  square  to  the  eye  ?  What  im- 
pressions are  those  which  have  been  associated  with  a 
visible  triangle,  so  that  the  revival  of  the  impressions 
revives  the  notion  of  the  triangle  ?  Brown  has  nowhere 
pointed  out  such  perceptions  and  impressions ;  nor  indeed 
was  it  possible  for  him  to  do  so ;  for  the  only  visual  per- 
ceptions which  he  allows  to  remain,  those  of  colour,  most 
assuredly  do  not  suggest  visible  figures  by  their  differ- 
ences ;  red  is  not  associated  with  square  rather  than  with 
round,  or  with  round  rather  than  square.  On  the  con- 
trary, the  eye,  constructed  in  a  very  complex  and  wonderful 
manner  in  order  that  it  may  give  to  us  directly  the  per- 
ception of  position  as  well  as  of  colour,  has  it  for  one  of  its 
prerogatives  to  give  us  this  information ;  and  the  percep- 
tion of  the  relative  position  of  each  part  of  the  visible 
boundary  of  an  object  constitutes  the  perception  of  its 
apparent  figure ;  which  faculty  we  cannot  deny  to  the  eye 
without  rejecting  the  plain  and  constant  evidence  of  our 
senses,  making  the  mechanism  of  the  eye  unmeaning, 
confounding  the  object  with  the  means  of  vision,  and 
rendering  the  mental  process  of  vision  utterly  unintelli- 
gible. 

Having  sufficiently  discussed  the  processes  of  percep- 
tion, I  now  return  to  the  consideration  of  the  Ideas  which 
these  processes  assume. 


295 


CHAPTER  III. 

SUCCESSIVE  ATTEMPTS  AT  THE  SCIENTIFIC 

APPLICATION  OF  THE  IDEA  OF  A 

MEDIUM. 

1.  IN  what  precedes,  we  have  shown  by  various  consi- 
derations that  we  necessarily  and  universally  assume  the 
perception  of  secondary  qualities  to  take  place  by  means 
of  a  medium  interjacent  between   the  object   and   the 
person   perceiving.      Perception   is   affected   by  various 
peculiarities,  according  to  the  nature  of  the  quality  per- 
ceived :    but  in  all  cases  a  medium  is  equally  essential  to 
the  process. 

This  principle,  which,  as  we  have  seen,  is  accepted  as 
evident  by  the  common  understanding  of  mankind,  is 
confirmed  by  all  additional  reflection  and  discipline  of 
the  mind,  and  is  the  foundation  of  all  the  theories  which 
have  been  proposed  concerning  the  processes  by  which  the 
perception  takes  place,  and  concerning  the  modifications 
of  the  qualities  thus  perceived.  The  medium,  and  the 
mode  in  which  the  impression  is  conveyed  through  the 
medium,  seem  to  be  different  for  different  qualities ;  but 
the  existence  of  the  medium  leads  to  certain  necessary 
conditions  or  alternatives,  which  have  successively  made 
their  appearance  in  science,  in  the  course  of  the  attempts 
of  men  to  theorize  concerning  the  principal  secondary 
qualities,  sound,  light,  and  heat.  We  must  now  point 
out  some  of  the  ways,  at  first  imperfect  and  erroneous, 
in  which  the  consequences  of  the  fundamental  assumption 
were  traced. 

2.  Sound. — In   all   cases  the  medium  of  sensation, 
whatever  it  is,  is  supposed  to  produce  the  effect  of  con- 
veying secondary  qualities  to  our  perception  by  means  of 
its  primary  qualities.     It  was  conceived  to  operate  by  the 


296      PHILOSOPHY  OF  SECONDARY  MECHANICAL  SCIENCES. 

size,  form,  and  motion  of  its  parts.  This  is  a  fundamental 
principle  of  the  class  of  sciences  of  which  we  have  at 
present  to  speak. 

It  was  assumed  from  the  first,  as  we  have  seen  in  the 
passage  lately  quoted  from  Aristotle  *,  that  in  the  convey- 
ance of  sound,  the  medium  of  communication  was  the  air. 
But  although  the  first  theorists  were  right  so  far,  that 
circumstance  did  not  prevent  their  going  entirely  wrong 
when  they  had  further  to  determine  the  nature  of  the 
process.  It  was  conceived  by  Aristotle  that  the  air  acted 
after  the  manner  of  a  rigid  body; — like  a  staff,  which, 
receiving  an  impulse  at  one  end,  transmits  it  to  the 
other.  Now  this  is  altogether  an  erroneous  view  of  the 
manner  in  which  the  air  conveys  the  impulse  by  which 
sound  is  perceived.  An  approach  was  made  to  the  true 
view  of  this  process,  by  assimilating  it  to  the  diffusion  of 
the  little  circular  waves  which  are  produced  on  the  sur- 
face of  still  water  when  a  stone  is  dropt  into  it.  These 
little  waves  begin  from  the  point  thus  disturbed,  and  run 
outwards,  expanding  on  every  side,  in  concentric  circles, 
till  they  are  lost.  The  propagation  of  sound  through  the 
air  from  the  point  where  it  is  produced,  was  compared 
by  Vitruvius  to  this  diffusion  of  circular  waves  in  water ; 
and  thus  the  notion  of  a  propagation  of  impulse  by  the 
waves  of  a  fluid  was  introduced,  in  the  place  of  the  former 
notion  of  the  impulse  of  an  unyielding  body. 

But  though,  taking  an  enlarged  view  of  the  nature  of 
the  progress  of  a  wave,  this  is  a  just  representation  of  the 
motion  of  air  in  conveying  sound,  we  cannot  suppose  that 
the  process  was,  at  the  period  of  which  we  speak,  rightly 
understood.  For  the  waves  of  water  were  contemplated 
only  as  affecting  the  surface  of  the  water ;  and  as  the  air 
has  no  surface,  the  communication  must  take  place  by 
means  of  an  internal  motion,  which  can  bear  only  a 
remote  and  obscure  resemblance  to  the  waves  which  we 

*  Supr.,  p.  271. 


SCIENTIFIC  APPLICATION  OF  THE  IDEA  OF  A  MEDIUM.     297 

see.  And  even  with  regard  to  the  waves  of  water,  the 
mechanism  by  which  they  are  produced  and  transferred 
was  not  at  all  understood ;  so  that  the  comparison 
employed  by  Vitruvius  must  be  considered  rather  as  a 
loose  analogy  than  as  an  exact  scientific  explanation. 

No  correct  account  of  such  motions  was  given,  till 
the  formation  of  the  science  of  mechanics  in  modern 
times  had  enabled  philosophers  to  understand  more  dis- 
tinctly the  mode  in  which  motion  is  propagated  through 
a  fluid,  and  to  discern  the  forces  which  the  process  calls 
into  play,  so  as  to  continue  the  motion  once  begun. 
Newton  introduced  into  this  subject  the  exact  and  rigor- 
ous conception  of  an  undulation,  which  is  the  true  key  to 
the  explanation  of  impulses  conveyed  through  a  fluid. 

Even  at  the  present  day,  the  right  apprehension  of 
the  nature  of  an  undulation  transmitted  through  a  fluid 
is  found  to  be  very  difficult  for  all  persons  except  those 
whose  minds  have  been  duly  disciplined  by  mathematical 
studies.  When  we  see  a  wave  run  along  the  surface  of 
water,  we  are  apt  to  imagine  at  first  that  a  portion  of  the 
fluid  is  transferred  bodily  from  one  place  to  another. 
But  with  a  little  consideration  we  may  easily  satisfy  our- 
selves that  this  is  not  so:  for  if  we  look  at  a  field  of 
standing  corn,  when  a  breeze  blows  over  it,  we  see  waves 
like  those  of  water  run  along  its  surface.  Yet  it  is  clear 
that  in  this  case  the  separate  stalks  of  corn  only  bend 
backwards  and  forwards,  and  no  portion  of  the  grain  is 
really  conveyed  from  one  part  of  the  field  to  the  other. 
This  is  obvious  even  to  popular  apprehension.  The  poet 
speaks  of 

The  rye, 

That  stoops  its  head  when  whirlwinds  rave 
And  springs  again  in  eddying  wave 
As  each  wild  gust  sweeps  by. 

Each   particle  of  the  mass    in  succession   has  a  small 


298      PHILOSOPHY  OF  SECONDARY  MECHANICAL  SCIENCES. 

motion  backwards  and  forwards;  and  by  this  means  a 
large  ridge  made  by  many  such  particles  runs  along  the 
mass  to  any  distance.  This  is  the  general  notion  of  an 
undulation. 

Thus,  when  an  undulation  is  propagated  in  a  fluid, 
it  is  not  matter,  but  form,  which  is  transmitted  from  one 
place  to  another.  The  particles  along  the  line  of  each 
wave  assume  a  certain  arrangement,  and  this  arrangement 
passes  from  one  part  to  another,  the  particles  changing 
their  places  only  within  narrow  limits,  so  as  to  lend 
themselves  successively  to  the  arrangements  by  which 
the  successive  waves,  and  the  intervals  between  the 
waves,  are  formed. 

When  such  an  undulation  is  propagated  through  air, 
the  wave  is  composed,  not,  as  in  water,  of  particles  which 
are  higher  than  the  rest,  but  of  particles  which  are  closer 
to  each  other  than  the  rest.  The  wave  is  not  a  ridge  of 
elevation,  but  a  line  of  condensation ;  and  as  in  water 
wre  have  alternately  elevated  and  depressed  lines,  we  have 
in  air  lines  alternately  condensed  and  rarefied.  And  the 
motion  of  the  particles  is  not,  as  in  water,  up  and  down? 
in  a  direction  transverse  to  that  of  the  wave  which  runs 
forwards ;  in  the  motion  of  an  undulation  through  air  the 
motion  of  each  particle  is  alternately  forwards  and  back- 
wards, while  the  motion  of  the  undulation  is  constantly 
forwards. 

This  precise  and  detailed  account  of  the  undulatory 
motion  of  air  by  which  sound  is  transmitted  was  first 
given  by  Newton.  He  further  attempted  to  determine 
the  motions  of  the  separate  particles,  and  to  point  out 
the  force  by  which  each  particle  affects  the  next,  so  as 
to  continue  the  progress  of  the  undulation  once  begun. 
The  motions  of  each  particle  must  be  oscillatory;  he 
assumed  the  oscillations  to  be  governed  by  the  simplest 
law  of  oscillation  which  had  come  under  the  notice  of 


SCIENTIFIC  APPLICATION  OF  THE  IDEA  OF  A  MEDIUM.     299 

mathematicians,  (that  of  small  vibrations  of  a  pendulum;) 
and  he  proved  that  in  this  manner  the  forces  which  are 
called  into  play  by  the  contraction  and  expansion  of  the 
parts  of  the  elastic  fluid  are  such  as  the  continuance  of 
the  motion  requires. 

Newton's  proof  of  the  exact  law  of  oscillatory  motion 
of  the  aerial  particles  was  not  considered  satisfactory  by 
succeeding  mathematicians;  for  it  was  found  that  the 
same  result,  the  development  of  forces  adequate  to  con- 
tinue the  motion,  would  follow  if  any  other  law  of  the 
motion  were  assumed.  Cramer  proved  this  by  a  sort  of 
parody  of  Newton's  proof,  in  which,  by  the  alteration  of 
a  few  phrases  in  this  formula  of  demonstration,  it  was 
made  to  establish  an  entirely  different  conclusion. 

But  the  general  conception  of  an  undulation  as  pre- 
sented by  Newton  was,  as  from  its  manifest  mechanical 
truth  it  could  not  fail  to  be,  accepted  by  all  mathemati- 
cians :  and  in  proportion  as  the  methods  of  calculating 
the  motions  of  fluids  were  further  improved,  the  neces- 
sary consequences  of  this  conception,  in  the  communica- 
tion of  sound  through  air,  were  traced  by  unexceptionable 
reasoning.  This  was  especially  done  by  Euler  and 
Lagrange,  whose  memoirs  on  such  motions  of  fluids  are 
some  of  the  most  admirable  examples  which  exist,  of 
refined  mathematical  methods  applied  to  the  solution  of 
difficult  mechanical  problems. 

But  the  great  step  in  the  formation  of  the  theory  of 
sound  was  undoubtedly  that  which  we  have  noticed,  the 
introduction  of  the  conception  of  an  undulation  such  as 
we  have  attempted  to  describe  it : — a  state,  condition,  or 
arrangement  of  the  particles  of  a  fluid,  which  is  trans- 
ferred from  one  part  of  space  to  another  by  means  of 
small  motions  of  the  particles  altogether  distinct  from 
the  movement  of  the  undulation  itself.  This  is  a  con- 
ception which  is  not  obvious  to  common  apprehension* 


300      PHILOSOPHY  OF  SECONDARY  MECHANICAL  SCIENCES. 

It  appears  paradoxical  at  first  sight  to  speak  of  a  large 
wave  (as  the  tide  wave)  running  up  a  river  at  the  rate  of 
twenty  miles  an  hour,  while  the  stream  of  the  river  is 
all  the  while  flowing  downwards.  Yet  this  is  a  very 
common  fact.  And  the  conception  of  such  a  motion 
must  be  fully  mastered  by  all  who  would  reason  rightly 
concerning  the  transmission  of  impressions  through  a 
medium. 

We  have  described  the  motion  of  sound  as  produced 
by  small  motions  of  the  particles  forwards  and  backwards, 
while  the  waves,  or  condensed  and  rarefied  lines,  move 
constantly  forwards.  It  may  be  asked  what  right  we 
have  to  suppose  the  motion  to  be  of  this  kind,  since 
when  sound  is  heard  no  such  motions  of  the  particles  of 
air  can  be  observed,  even  by  refined  methods  of  observa- 
tion.  Thus  Bacon  declares  himself  against  the  hypothesis 
of  such  a  vibration,  since,  as  he  remarks,  it  cannot  be 
perceived  in  any  visible  impression  upon  the  flame  of  a 
candle.  And  to  this  we  reply,  that  the  supposition  of 
this  vibration  is  made  in  virtue  of  a  principle  which  is 
involved  in  the  original  assumption  of  a  medium ;  namely, 
That  a  medium,  in  conveying  secondary  qualities,  operates  by 
means  of  its  primary  qualities,  the  bulk,  figure,  motion, 
and  other  mechanical  properties  of  its  parts.  This  is  an 
axiom  belonging  to  the  Idea  of  a  Medium.  In  virtue 
of  this  axiom  it  is  demonstrable  that  the  motion  of  the 
air,  when  any  how  disturbed,  must  be  such  as  is  supposed 
in  our  acoustical  reasonings.  For  the  elasticity  of  the 
parts  of  the  air,  called  into  play  by  its  expansion  and 
contraction,  lead,  by  a  mechanical  necessity,  to  such  a 
motion  as  we  have  described.  We  may  add  that,  by 
proper  contrivances,  this  motion  may  be  made  percep- 
tible in  its  visible  effects.  Thus  the  theory  of  sound, 
as  an  impression  conveyed  through  air,  is  established 
upon  evident  general  principles,  although  the  mathe- 


SCIENTIFIC  APPLICATION  OF  THE  IDEA  OF  A  MEDIUM.     301 

rnatical  calculations  which  are  requisite  to  investigate 
its  consequences  are,  some  of  them,  of  a  very  recondite 
kind. 

3.  Light. — The  early  attempts  to  explain  vision  repre- 
sented it  as  performed  by  means  of  material  rays  pro- 
ceeding from  the  eye,  by  the  help  of  which  the  eye  felt 
out  the  form  and  other  visible  qualities  of  an  object,  as  a 
blind  man  might  do  with  his  staff.  But  this  opinion 
could  not  keep  its  ground  long :  for  it  did  not  even 
explain  the  fact  that  light  is  necessary  to  vision.  Light 
as  a  peculiar  medium  was  then  assumed  as  the  machinery 
of  vision ;  but  the  mode  in  which  the  impression  was 
conveyed  through  the  medium  was  left  undetermined, 
and  no  advance  was  made  towards  sound  theory,  on  that 
subject,  by  the  ancients. 

In  modern  times,  when  the  prevalent  philosophy 
began  to  assume  a  mechanical  turn  (as  in  the  theories  of 
Descartes),  light  was  conceived  to  be  a  material  substance 
which  is  emitted  from  luminous  bodies,  and  which  is  also 
conveyed  from  all  bodies  to  the  eye,  so  as  to  render  them 
visible.  The  various  changes  of  direction  by  which  the 
rays  of  light  are  affected,  (reflection,  refraction,  &c.) 
Descartes  explained,  by  considering  the  particles  of  light 
as  small  globules,  which  change  their  direction  when 
they  impinge  upon  other  bodies,  according  to  the  laws  of 
mechanics.  Newton,  with  a  much  more  profound  know- 
ledge of  mechanics  than  Descartes  possessed,  adopted,  in 
the  most  mature  of  his  speculations,  nearly  the  same 
view  of  the  nature  of  light ;  and  endeavoured  to  show 
that  reflection,  refraction,  and  other  properties  of  light, 
might  be  explained  as  the  effects  which  certain  forces, 
emanating  from  the  particles  of  bodies,  produce  upon  the 
luminiferous  globules. 

But  though  some  of  the  properties  of  light  could  thus 
be  accounted  for  by  the  assumption  of  particles  emitted 
from  luminous  bodies,  and  reflected  or  refracted  by  forces, 


302      PHILOSOPHY  OF  SECONDARY  MECHANICAL  SCIENCES. 

other  properties  came  into  view  which  would  not  admit 
of  the  same  explanation.  The  phenomena  of  diffraction 
.(the  fringes  which  accompany  shadows)  could  never  be 
truly  represented  by  such  an  hypothesis,  in  spite  of  many 
attempts  which  were  made.  And  the  colours  of  thin 
plates,  which  show  the  rays  of  light  to  be  affected  by  an 
alternation  of  two  different  conditions  at  small  intervals 
along  their  length,  led  Newton  himself  to  incline,  often 
and  strongly,  to  some  hypothesis  of  undulation.  The 
double  refraction  of  Iceland  spar,  a  phenomenon  in  itself 
very  complex,  could,  it  was  found  by  Huyghens,  be 
expressed  with  great  simplicity  by  a  certain  hypothesis  of 
undulations. 

Two  hypotheses  of  the  nature  of  the  luminiferous 
medium  were  thus  brought  under  consideration ;  the  one 
representing  light  as  matter  emitted  from  the  luminous 
object,  the  other,  as  undulations  propagated  through  a  fluid. 
These  two  hypotheses  remained  in  presence  of  each  other 
during  the  whole  of  the  last  century,  neither  of  them 
gaining  any  material  advantage  over  the  other,  though  the 
greater  part  of  mathematicians,  following  Newton,  em- 
braced the  emission  theory.  But  at  the  beginning  of  the 
present  century,  an  additional  class  of  phenomena,  those 
of  the  interference  of  two  rays  of  light,  were  brought 
under  consideration  by  Dr.  Young ;  and  these  phenomena 
were  strongly  in  favour  of  the  undulatory  theory,  while 
they  were  irreconcilable  with  the  hypothesis  of  emission. 
If  it  had  not  been  for  the  original  bias  of  Newton  and  his 
school  to  the  other  side,  there  can  be  little  doubt  that 
from  this  period  light  as  well  as  sound  would  have  been 
supposed  to  be  propagated  by  undulations ;  although  in 
this  case  it  was  necessary  to  assume  as  the  vehicle  of 
such  undulations  a  special  medium  or  ether.  Several 
points  of  the  phenomena  of  vision  no  doubt  remained 
unexplained  by  the  undulatory  theory,  as  absorption,  and 
the  natural  colours  of  bodies;  but  such  facts,  though 


SCIENTIFIC  APPLICATION  OF  THE  IDEA  OF  A  MEDIUM.    303 

they  did  not  confirm,  did  not  evidently  contradict  the 
theory  of  a  luminiferous  ether  ;  and  the  facts  which  such 
a  theory,  did  explain,  it  explained  with  singular  happiness 
and  accuracy. 

But  before  this  undulatory  theory  could  be  generally 
accepted,  it  was  presented  in  an  entirely  new  point  of 
view  by  being  combined  with  the  facts  of  polarization. 
The  general  idea  of  polarization  must  be  illustrated  here- 
after ;  but  we  may  here  remark  that  Young  and  Fresnel, 
who  had  adopted  the  undulatory  theory,  after  being 
embarrassed  for  some  time  by  the  new  facts  which  were 
thus  presented  to  their  notice,  at  last  saw  that  these 
facts  might  be  explained  by  conceiving  the  vibrations  to 
be  transverse  to  the  ray,  the  motions  of  the  particles 
being  not  backwards  and  forwards  in  the  line  in  which 
the  impulse  travels,  but  to  the  right  and  left  of  that  line. 
This  conception  of  transverse  vibrations,  though  quite 
unforeseen,  had  nothing  in  it  which  was  at  all  difficult  to 
reconcile  with  the  general  notion  of  an  undulation.  We 
have  described  an  undulation,  or  wave,  as  a  certain 
condition  or  arrangement  of  the  particles  of  the  fluid 
successively  transferred  from  one  part  of  space  to 
another :  and  it  is  easily  conceivable  that  this  arrange- 
ment or  wave  may  be  produced  by  a  lateral  transfer  of 
the  particles  from  their  quiescent  positions.  This  con- 
ception of  transverse  vibrations  being  accepted,  it  was 
found  that  the  explanation  of  the  phenomena  of  polariza- 
tion and  of  those  of  interference  led  to  the  same  theory 
with  a  correspondence  truly  wonderful ;  and  this  coinci- 
dence in  the  views  collected  from  two  quite  distinct 
classes  of  phenomena  was  justly  considered  as  an  almost 
demonstrative  evidence  of  the  truth  of  this  undulatory 
theory. 

It  remained  to  be  considered  whether  the  doctrine  of 
transverse  vibrations  in  a  fluid  could  be  reconciled  with 


304      PHILOSOPHY  OF  SECONDARY  MECHANICAL  SCIENCES. 

the  principles  of  mechanics.  And  it  was  found  that  by 
making  certain  suppositions,  in  which  no  inherent  impro- 
bability existed,  the  hypothesis  of  transverse  vibrations 
would  explain  the  laws,  both  of  interference  and  of 
polarization  of  light,  in  air  and  in  crystals  of  all  kinds, 
with  a  surprising  fertility  and  fidelity. 

Thus  the  undulatory  theory  of  light,  like  the  undu- 
latory  theory  of  sound,  is  recommended  by  its  conformity 
to  the  fundamental  principle  of  the  Secondary  Mechanical 
Sciences,  that  the  medium  must  be  supposed  to  transmit 
its  peculiar  impulses  according  to  the  laws  of  mechanics. 
Although  no  one  had  previously  dreamt  of  qualities  being 
conveyed  through  a  medium  by  such  a  process,  yet  when  it 
is  once  suggested  as  the  only  mode  of  explaining  some  of 
the  phenomena,  there  is  nothing  to  prevent  our  accepting 
it  entirely,  as  a  satisfactory  theory  for  all  the  known  laws 
of  light. 

4.  Heat. — With  regard  to  heat  as  with  regard  to 
light,  a  fluid  medium  was  necessarily  assumed  as  the 
vehicle  of  the  property.  During  the  last  century,  this 
medium  was  supposed  to  be  an  emitted  fluid.  And 
many  of  the  ascertained  Laws  of  Heat,  those  which 
prevail  with  regard  to  its  radiation  more  especially,  were 
well  explained  by  this  hypothesis*.  Other  effects  of  heat, 
however,  as  for  instance  latent  lieat\>  and  the  change  of 
consistence  of  bodies  {,  were  not  satisfactorily  brought  into 
connexion  with  the  hypothesis ;  while  conduction  §,  which 
at  first  did  not  appear  to  result  from  the  fundamental 
assumption,  was  to  a  certain  extent  explained  as  internal 
radiation. 

But  it  was  by  no  means  clear  that  an  undulatory 
theory  of  heat  might  not  be  made  to  explain  these 
phenomena  equally  well.  Several  philosophers  inclined 

*  See  the  Account  of  the  Theory  of  Exchanges,  Hist.  Ind.  Set.,  ii.  474. 
t  /£.,  ii.  499.  t  Ib.,  498.  §  Ib.9  469. 


SCIENTIFIC  APPLICATION  OF  THE  IDEA  OF  A  MEDIUM.     305 

to  such  a  theory ;  and  finally,  Ampere  showed  that  the 
doctrine  that  the  heat  of  a  body  consists  in  the  undula- 
tions of  its  particles  propagated  by  means  of  the  undula- 
tions of  a  medium,  might  be  so  adjusted  as  to  explain  all 
which  the  theory  of  emission  could  explain,  and  moreover 
to  account  for  facts  and  laws  which  were  out  of  the  reach 
of  that  theory.  About  the  same  time  it  was  discovered 
by  Prof.  Forbes  and  M.  Nobili  that  radiant  heat  is,  under 
certain  circumstances,  polarized.  Now  polarization  had 
been  most  satisfactorily  explained  by  means  of  transverse 
undulations  in  the  case  of  light ;  while  all  attempts  to 
modify  the  emission  theory  so  as  to  include  polarization 
in  it,  had  been  found  ineffectual.  Hence  this  discovery 
was  justly  considered  as  lending  great  countenance  to  the 
opinion  that  heat  consists  in  the  vibrations  of  its  proper 
medium. 

But  what  is  this  medium  ?  Is  it  the  same  by  which 
the  impressions  of  light  are  conveyed  ?  This  is  a  difficult 
question ;  or  rather  it  is  one  which  we  cannot  at  pre- 
sent hope  to  answer  with  certainty.  No  doubt  the 
connexion  between  light  and  heat  is  so  intimate  and 
constant,  that  we  can  hardly  refrain  from  considering 
them  as  affections  of  the  same  medium.  But  instead  of 
attempting  to  erect  our  systems  on  such  loose  and 
general  views  of  connexion,  it  is  rather  the  business  of 
the  philosophers  of  the  present  day  to  determine  the  laws 
of  the  operation  of  heat,  and  its  real  relation  to  light,  in 
order  that  we  may  afterwards  be  able  to  connect  the 
theories  of  the  two  qualities.  Perhaps  in  a  more 
advanced  state  of  our  knowledge  we  may  be  able  to  state 
it  as  an  axiom,  that  two  secondary  qualities,  which  are 
intimately  connected  in  their  causes  and  effects,  must  be 
affections  of  the  same  medium.  But  at  present  it  does 
not  appear  safe  to  proceed  upon  such  a  principle,  although 
many  writers,  in  their  speculations  both  concerning  light 
VOL.  i.  x 


306      PHILOSOPHY  OF  SECONDARY  MECHANICAL  SCIENCES. 

and  beat,   and   concerning    other   properties,  have    not 
hesitated  to  do  so. 

Some  other  consequences  follow  from   the  Idea  of  a 
Medium  which  must  be  the  subject  of  another  chapter. 


CHAPTER  IV. 
OF  THE  MEASURE  OF  SECONDARY  QUALITIES. 

1.  Scales  of  Qualities  in  general. — The  ultimate 
object  of  our  investigation  in  each  of  the  Secondary 
Mechanical  Sciences,  is  the  nature  of  the  processes  by 
which  the  special  impressions  of  sound,  light,  and  heat,  are 
conveyed,  and  the  modifications  of  which  these  processes 
are  susceptible.  And  of  this  investigation,  as  we  have 
seen,  the  necessary  basis  is  the  principle,  that  these 
impressions  are  transmitted  by  means  of  a  medium. 
But  before  we  arrive  at  this  ultimate  object,  we  may  find 
it  necessary  to  occupy  ourselves  with  several  intermediate 
objects :  before  we  discover  the  cause,  it  may  be  necessary 
to  determine  the  laws  of  the  phenomena.  Even  if  we 
cannot  immediately  ascertain  the  mechanism  of  light  or 
heat,  it  may  still  be  interesting-  and  important  to  arrange 
and  measure  the  effects  which  we  observe. 

The  idea  of  a  medium  affects  our  proceeding  in  this 
research  also.  We  cannot  measure  secondary  qualities 
in  the  same  manner  in  which  we  measure  primary  quali- 
ties, by  a  mere  addition  of  parts.  There  is  this  leading 
and  remarkable  difference,  that  while  both  classes  of 
qualities  are  susceptible  of  changes  of  magnitude,  primary 
qualities  increase  by  addition  of  extension,  secondary,  by 
augmentation  of  intensity.  A  space  is  doubled  when 
another  equal  space  is  placed  by  its  side;  one  weight 
joined  to  another  makes  up  the  sum  of  the  two.  But 


MEASURE  OF  SECONDARY  QUALITIES.  007 

when  one  degree  of  warmth  is  combined  with  another,  or 
one  shade  of  red  colour  with  another,  we  cannot  in  like 
manner  talk  of  the  sum.  The  component  parts  do  not 
evidently  retain  their  separate  existence;  we  cannot 
separate  a  strong  green  colour  into  two  weaker  ones,  as 
we  can  separate  a  large  force  into  two  smaller.  The 
increase  is  absorbed  into  the  previous  amount,  and  is  no 
longer  in  evidence  as  a  part  of  the  whole.  And  this  is 
the  difference  which  has  given  birth  to  the  two  words 
extended,  and  intense.  That  is  extended  which  has  "partes 
extra  partes,"  parts  outside  of  parts  :  that  is  intense  which 
becomes  stronger  by  some  indirect  and  unapparent  increase 
of  agency,  like  the  stretching  of  the  internal  springs  of  a 
machine,  as  the  term  intense  implies.  Extended  magni- 
tudes can  at  will  be  resolved  into  the  parts  of  which  they 
were  originally  composed,  or  any  other  which  the  nature 
of  their  extension  admits ;  their  proportion  is  apparent ; 
they  are  directly  and  at  once  subject  to  the  relations  of 
number.  Intensive  magnitudes  cannot  be  resolved  into 
.smaller  magnitudes ;  we  can  see  that  they  differ,  but  we 
cannot  tell  in  what  proportion ;  we  have  no  direct 
measure  of  their  quantity.  How  many  times  hotter  than 
blood  is  boiling  water?  The  answer  cannot  be  given 
by  the  aid  of  our  feelings  of  heat  alone. 

This  difference,  as  we  have  said,  is  connected  with 
the  fundamental  principle  that  we  do  not  perceive 
secondary  qualities  directly,  but  through  a  medium.  We 
have  no  natural  apprehension  of  light,  or  sound,  or  heat, 
as  they  exist  in  the  bodies  from  which  they  proceed,  but 
only  as  they  affect  our  organs.  We  can  only  measure 
them,  therefore,  by  some  scale  supplied  by  their  effects. 
And  thus  while  extended  magnitudes,  as  space,  time,  are 
measurable  directly  and  of  themselves;  intensive  magni- 
tudes, as  brightness,  loudness,  heat,  are  measurable  only 
by  artificial  means  and  conventional  scales.  Space,  time, 

X  2 


308      PHILOSOPHY  OF  SECONDARY  MECHANICAL  SCIENCES. 

measure  themselves :  the  repetition  of  a  smaller  space,  or 
time,  while  it  composes  a  larger  one,  measures  it.  But 
for  light  and  heat  we  must  have  photometers  and  ther- 
mometers, which  measure  something  which  is  assumed  to 
be  an  indication  of  the  quality  in  question.  In  one  case, 
the  mode  of  applying  the  measure,  and  the  meaning  of 
the  number  resulting,  are  seen  by  intuition ;  in  the 
other,  they  are  consequences  of  assumption  and  reason- 
ing. In  the  one  case,  they  are  units,  of  which  the  exten- 
sion is  made  up ;  in  the  other,  they  are  degrees  by  which 
the  intensity  ascends. 

2.  When  we  discover  any  property  in  a  sensible  qua- 
lity, which  at  once  refers  us  to  number  or  space,  we  readily 
take  this  property  as  a  measure ;  and  thus  we  make  a 
transition  from  quality  to  quantity.  Thus  Ptolemy  in  the 
third  chapter  of  the  First  Book  of  his  Harmonics  begins 
thus :  "  As  to  the  differences  which  exist  in  sounds  both 
in  quality  and  in  quantity,  if  we  consider  that  difference 
which  refers  to  the  acuteness  and  graveness,  we  cannot 
at  once  tell  to  which  of  the  above  two  classes  it  belongs, 
till  we  have  considered  the  causes  of  such  symptoms." 
But  at  the  end  of  the  chapter,  having  satisfied  himself 
that  grave  sounds  result  from  the  magnitude  of  the  string 
or  pipe,  other  things  being  equal,  he  infers,  "  Thus  the 
difference  of  acute  and  grave  appears  to  be  a  difference  of 
quantity'' 

In  the  same  manner,  in  order  to  form  Secondary 
Mechanical  Sciences  respecting  any  of  the  other  pro- 
perties of  bodies,  we  must  reduce  these  properties  to  a 
dependence  upon  quantity,  and  thus  make  them  subject 
to  measurement.  We  cannot  obtain  any  sciential  truths 
respecting  the  comparison  of  sensible  qualities,  till  we 
have  discovered  measures  and  scales  of  the  qualities 
which  we  have  to  consider ;  and  accordingly,  some  of  the 
most  important  steps  in  such  sciences  have  been  the 


MEASURE  OF  SECONDARY  QUALITIES.  809 

establishment  of  such  measures  and  scales,  and  the  inven- 
tion of  the  requisite  instruments. 

The  formation  of  the  mathematical  sciences  which 
rest  upon  the  measures  of  the  intensity  of  sensible 
qualities  took  place  mainly  in  the  course  of  the  last 
century.  Perhaps  we  may  consider  Lambert,  a  mathe- 
matician who  resided  in  Switzerland,  and  published  about 
1750,  as  the  person  who  first  clearly  felt  the  importance 
of  establishing  such  sciences.  His  Photometry,  Pyro- 
metry,  Hygrometry,  are  examples  of  the  systematic 
reduction  of  sensible  qualities  (light,  heat,  moisture)  to 
modes  of  numerical  measurement. 

We  now  proceed  to  speak  of  such  modes  of  measure- 
ment with  regard  to  the  most  obvious  properties  of 
bodies. 

3.  (I.)  The  Musical  Scale. — The  establishment  of 
the  Harmonic  Canon,  that  is,  of  a  Scale  and  Measure  of 
the  musical  place  of  notes,  in  the  relation  of  high  and  low, 
was  the  first  step  in  the  science  of  Harmonics.  The 
perception  of  the  differences  and  relations  of  musical 
sounds  is  the  office  of  the  sense  of  hearing;  but  these 
relations  are  fixed,  and  rendered  accurately  recognisable 
by  artificial  means.  "Indeed,  in  all  the  senses,"  as 
Ptolemy  truly  says  in  the  opening  of  his  Harmonics,  "the 
sense  discovers  what  is  approximately  true,  and  receives 
accuracy  from  another  quarter :  the  reason  receives  the 
approximately-true  from  another  quarter,  and  discovers 
the  accurate  truth."  We  can  have  no  measures  of 
sensible  qualities  which  do  not  ultimately  refer  to  the 
sense ; — whether  they  do  this  immediately,  as  when  we 
refer  colours  to  an  assumed  standard ;  or  mediately,  as 
when  we  measure  heat  by  expansion,  having  previously 
found  by  an  appeal  to  sense  that  the  expansion 
increases  with  the  heat.  Such  relations  of  sensible 
qualities  cannot  be  described  in  words,  and  can  only  be 


310     PHILOSOPHY  OF  SECONDARY  MECHANICAL  SCIENCES. 

apprehended  by  their  appropriate  faculty.  The  faculty 
by  which  the  relations  of  sounds  are  apprehended  is  a 
musical  car  in  the  largest  acceptation  of  the  term.  In  this 
signification  the  faculty  is  nearly  universal  among  men ; 
for  all  persons  have  musical  ears  sufficiently  delicate  to 
understand  and  to  imitate  the  modulations  corresponding 
to  various  emotions  in  speaking ;  which  modulations 
depend  upon  the  succession  of  acuter  and  graver  tones. 
These  are  the  relations  now  spoken  of,  and  these  are 
plainly  perceived  by  persons  who  have  very  imperfect 
musical  ears,  according  to  the  common  use  of  the  phrase. 
But  the  relations  of  tones  which  occur  in  speaking  are 
somewhat  indefinite  ;  and  in  forming  that  musical  scale 
which  is  the  basis  of  our  science  upon  the  subject,  we 
take  the  most  definite  and  marked  of  such  relations  of 
notes ;  such  as  occur,  not  in  speaking  but  in  singing. 
Those  musical  relations  of  two  sounds  which  we  call  the 
octave,  the  fifth,  the  fourth,  the  third,  are  recognised  after 
a  short  familiarity  with  them.  These  chords  or  intervals 
are  perceived  to  have  each  a  peculiar  character,  which 
separates  them  from  the  relations  of  two  sounds  taken  at 
random,  and  makes  it  easy  to  know  them  when  sung  or 
played  on  an  instrument ;  and  for  most  persons,  not  diffi- 
cult to  sing  the  sounds  in  succession  exactly,  or  nearly 
correct.  These  musical  relations,  or  concords,  then,  are 
the  groundwork  of  our  musical  standard.  But  how  are 
we  to  name  these  indescribable  sensible  characters  ? 
how  to  refer,  with  unerring  accuracy,  to  a  type  which 
exists  only  in  our  own  perceptions  ?  We  must  have  for 
this  purpose  a  Scale  and  a  Standard. 

The  Musical  Scale  is  a  series  of  eight  notes,  ascend- 
ing by  certain  steps  from  the  first  or  key-note  to  the 
octave  above  it,  each  of  the  notes  being  fixed  by  such 
distinguishable  musical  relations  as  we  have  spoken  of 
above.  We  may  call  these  notes  c,  D,  E,  F,  a,  A,  B,  c ; 


MEASURE  OF  SECONDARY  QUALITIES.  311 

and  we  may  then  say  that  G  is  determined  by  its  being  a 
fifth  above  c ;  D  by  its  being  a  fourth  below  G ;  E  by  its 
being  a  third  above  C ;  and  similarly  of  the  rest.  It  will 
be  recollected  that  the  terms  &  fifth,  a  fourth,  a  third,  have 
hitherto  been  introduced  as  expressing  certain  simple  and 
indescribable  musical  relations  among  sounds,  which 
might  have  been  indicated  by  any  other  names.  Thus 
we  might  call  the  fifth  the  dominant,  and  the  fourth  the 
subdominant,  as  is  done  in  one  part  of  musical  science. 
But  the  names  we  have  used,  which  are  the  common 
ones,  are  in  fact  derived  from  the  number  of  notes  which 
these  intervals  include  in  the  scale  obtained  in  the  above 
manner.  The  notes  c,  D,  E,  F,  G,  being  five,  the  interval 
from  c  to  G  is  a  fifth,  and  so  of  the  rest.  The  fixation  of 
this  scale  gave  the  means  of  describing  exactly  any  note 
which  occurs  in  the  scale,  and  the  method  is  easily  appli- 
cable to  notes  above  and  below  this  range ;  for  in  a 
series  of  sounds  higher  or  lower  by  an  octave  than  this 
standard  series,  the  ear  discovers  a  recurrence  of  the 
same  relations  so  exact,  that  a  person  may  sometimes 
imagine  he  is  producing  the  same  notes  as  another  when 
he  is  singing  the  same  air  an  octave  higher.  Hence  the 
next  eight  notes  may  be  conveniently  denoted  by  a  repeti- 
tion of  the  same  letters,  as  the  first ;  thus,  c,  r>,  E,  F,  G,  A,  B, 
c,  d,  e,f,  y,  a,  b ;  and  it  is  easy  to  devise  a  continuation 
of  such  cycles.  And  other  admissible  notes  are  desig- 
nated by  a  further  modification  of  the  standard  ones,  as 
by  making  each  note  flat  or  sharp ;  which  modification  it 
is  not  necessary  here  to  consider,  since  our  object  is  only 
to  show  how  a  standard  is  attainable,  and  how  it  serves 
the  ends  of  science. 

We  may  observe,  however,  that  the  above  is  not  an 
exact  account  of  the  first,  or  early  Greek  scale ;  for  this 
scale  was  founded  on  a  primary  division  of  the  interval  of 
two  octaves  (the  extreme  range  which  it  admitted)  into 


312      PHILOSOPHY  OF  SECONDARY  MECHANICAL  SCIENCES. 

five  tetrachords,  each  tetrachord  including  the  interval  of 
a  fourth.  All  the  notes  of  this  series  had  different 
names  borrowed  from  this  division*  r  thus  mese  was  the 
middle  or  key-note ;  the  note  below  it  was  lichanos  meson, 
the  next  below  was  parypate  meson,  the  next  lower 
Ju/pate  meson.  The  fifth  above  mese  was  nete  diazeuy- 
menon,  the  octave  was  nete  hyperlolceon. 

4.  But  supposing  a  complete  system  of  such  denomi- 
nations established,  how  could  it  be  with  certainty  and 
rigour  applied  ?  The  human  ear  is  fallible,  the  organs  of 
voice  imperfectly  obedient ;  if  this  were  not  so,  there 
would  be  no  such  thing  as  a  cjood  ear  or  a  good  voice. 
What  means  can  be  devised  of  finding  at  will  a  perfect 
concord,  a  fifth  or  a  fourth  ?  Or  supposing  such  concords 
fixed  by  an  acknowledged  authority,  how  can  they  be 
referred  to,  and  the  authority  adduced  ?  How  can  we 
enact  a  Standard  of  sounds  ? 

A  Standard  was  discovered  in  the  Monochord.  A 
musical  string  properly  stretched,  may  be  made  to  pro- 
duce different  notes,  in  proportion  as  we  intercept  a 
longer  or  shorter  portion,  and  make  this  portion  vibrate. 
The  relation  of  the  length  of  the  strings  which  thus 
sound  the  two  notes  a  and  c  is  fixed  and  constant,  and 
the  same  is  true  of  all  other  notes.  Hence  the  musical 
interval  of  any  notes  of  which  we  know  the  places  in  the 
musical  scale,  may  be  reproduced  by  measuring  the 
lengths  of  string  which  are  known  to  give  them.  If  c  be 
of  the  length  180,  D  is  169,  E  is  144,  F  is  135,  G  is  320; 
and  thus  the  musical  relations  are  reduced  to  numerical 
relations,  and  the  monochord  is  a  complete  and  perfect 
tonometer. 

We  have  here  taken  the  length  of  the  string  as  the  mea- 
sure of  the  tone :  but  we  may  observe  that  there  is  in  us  a 
necessary  tendency  to  assume  that  the  ground  of  this  mea- 

*  BURNEY'S  History  of  Music ,  vol.  i.  p.  28. 


MEASURE  OF  SECONDARY  QUALITIES.  313 

sure  is  to  be  sought  in  some  ulterior  cause  ;  and  when  we 
consider  the  matter  further,  we  find  this  cause  in  the  fre- 
quency of  these  vibrations  of  the  string.  The  truth  that 
the  same  note  must  result  from  the  same  frequency  of 
vibration  is  readily  assented  to  on  a  slight  suggestion  of 
experience.  Thus  Mersenne*,  when  he  undertakes  to 
determine  the  frequency  of  vibrations  of  a  given  sound, 
says  "  Supponendum  est  quoscunque  nervos  et  quaslibet 
chordas  unisonum  facientes  eundem  efficere  numerum 
recursuum  eodem  vel  equali  tempore,  quod  perpetua 
constat  experientia."  And  he  proceeds  to  apply  it  to 
cases  where  experience  could  not  verify  this  assertion,  or 
at  least  had  not  verified  it,  as  to  that  of  pipes. 

The  pursuit  of  these  numerical  relations  of  tones 
forms  the  science  of  Harmonics ;  of  which  here  we  do 
not  pretend  to  give  an  account,  but  only  to  show,  how 
the  invention  of  a  Scale  and  Nomenclature,  a  Standard 
and  Measure  of  the  tone  of  sounds,  is  its  necessary  basis. 
We  will  therefore  nowr  proceed  to  speak  of  another 
subject;  colour. 

5.  (II.)  Scales  of  Colour. — The  Prismatic  Scale  of 
Colour. — A  Scale  of  Colour  must  depend  originally  upon 
differences  discernible  by  the  eye,  as  a  scale  of  notes 
depends  on  differences  perceived  by  the  ear.  In  one 
respect  the  difficulty  is  greater  in  the  case  of  the  visible 
qualities,  for  ,there  are  no  relations  of  colour  which  the 
eye  peculiarly  singles  out  and  distinguishes,  as  the  ear 
selects  and  distinguishes  an  octave  or  a  fifth.  Hence  we 
are  compelled  to  take  an  arbitrary  scale ;  and  we  have 
to  find  one  which  is  fixed,  and  which  includes  a  proper 
collection  of  colours.  The  prismatic  spectrum,  or  coloured 
image  produced  when '-a  small  beam  of  light  passes 
obliquely  through  any  transparent  surface  (as  the  surface 
of  a  prism  of  glass,)  offers  an  obvious  Standard  as  far 

*  Harmoma,  lib.  ii.  Prop,  19, 


314     PHILOSOPHY  OF  SECONDARY  MECHANICAL  SCIENCES. 


as  it  is  applicable.  Accordingly  colours  have,  for  various 
purposes,  been  designated. by  their  place  in  the  spectrum 
ever  since  the  time  of  Newton  ;  and  we  have  thus  a 
means  of  referring  to  such  colours  as  are  included  in  the 
series  red,  orange,  yellow,  green,  blue,  violet,  indigo,  and  the 
intermediate  tints. 

But  this  scale  is  not  capable  of  numerical  precision. 
If  the  spectrum  could  be  exactly  defined  as  to  its 
extremities,  and  if  these  colours  occupied  always  the 
same  proportional  part  of  it,  we  might  describe  any 
colour  in  the  above  series  by  the  measure  of  its  position. 
But  the  fact  is  otherwise.  The  spectrum  is  too  indefinite 
in  its  boundaries  to  afford  any  distinct  point  from  which 
we  may  commence  our  measures ;  and  moreover  the 
spectra  produced  by  different  transparent  bodies  differ 
from  each  other.  Newton  had  supposed  that  the  spec- 
trum and  its  parts  were  the  same,  so  long  as  the  refrac- 
tion was  the  same ;  but  his  successors  discovered  that, 
with  the  same  amount  of  refraction  in  different  kinds  of 
glass,  there  are  different  magnitudes  of  the  spectrum ; 
and  what  is  still  worse  with'  reference  to  our  present 
purpose,  that  the  spectra  from  different  glasses  have 
the  colours  distributed  in  different  proportions.  In  order, 
therefore,  to  make  the  spectrum  the  scale  of  colour,  we 
must  assume  some  fixed  substance ;  for  instance,  we  may 
take  water,  and  thus  the  colours  of  the  rainbow  will 
be  our  standard.  But  we  should  still  have  an  extreme 
difficulty  in  applying  such  a  rule.  The  distinctions  of 
colour  which  the  terms  of  common  language  express,  are 
not  used  with  perfect  unanimity  or  with  rigorous  precision. 
What  one  person  calls  bluish  green  another  calls  greenish 
blue.  Nobody  can  say  what  is  the  precise  boundary 
between  red  and  orange.  Thus  the  prismatic  scale  of 
colour  was  incapable  of  mathematical  exactness,  and  this 
inconvenience  was  felt  up  to  our  own  times. 


MEASURE  OF  SECONDARY  QUALITIES.  315 

But  this  difficulty  was  removed  by  a  curious  dis- 
covery of  Fraunhofer ;  who  found  that  there  are,  in  the 
solar  spectrum,  certain  line  black  Lines  which  occupy  a 
definite  place  in  the  series  of  colours,  and  can  be  ob- 
served with  perfect  precision.  We  have  now  no  uncer- 
tainty as  to  what  coloured  light  we  are  speaking  of,  when 
we  describe  it  as  that  part  of  the  spectrum  in  which 
Fraunhofer's  Line  c  or  D  occurs.  And  thus,  by  this  dis- 
covery, the  prismatic  spectrum  of  sunlight  became,  for 
certain  purposes,  an  exact  Chromatometer . 

6.  Newton's  Scale  of  Colours. — Still,  such  a  standard 
is  arbitrary  and  seemingly  anomalous.  The  lines  A,  B,  c,  D, 
&c.,  of  Fraunhofer's  spectrum  are  distributed  without 
any  apparent  order  or  law ;  and  we  do  not,  in  this  way, 
obtain  numerical  measures,  which  is  what,  in  all  cases,  we 
desire  to  have.  Another  discovery  of  Newton,  however, 
gives  us  a  spectrum  containing  the  same  colours  as  the 
prismatic  spectrum,  but  produced  in  another  way,  so  that 
the  colours  have  a  numerical  relation.  I  speak  of  the 
colours  of  thin  plates.  The  little  rainbows  which  we  some- 
times see  in  the  cracks  of  broken  glass  are  governed  by 
fixed  and  simple  laws.  The  kind  of  colour  produced  at 
any  point  depends  on  the  thickness  of  the  thin  plate  of 
air  included  in  the  fissure.  If  the  thickness  be  twelve- 
millionths  of  an  inch,  the  colour  is  orange,  if  ten-mil- 
lionths  of  an  inch,  we  have  green,  and  so  on ;  and  thus 
these  numbers  which  succeed  each  other  in  a  regular 
order  from  red  to  indigo,  give  a  numerical  measure  of 
each  colour ;  which  measure,  when  we  pursue  the  subject, 
we  find  is  one  of  the  bases  of  all  optical  theory.  The 
series  of  colours  obtained  from  plates  of  air  of  gradually 
increasing  thickness  is  called  Newton's  Scale  of  Colours; 
but  we  may  observe  that  this  is  not  precisely  what  we  are 
here  speaking  of,  a  scale  of  simple  colours ;  it  is  a  series 
produced  by  certain  combinations,  resulting  from  the 


316      PHILOSOPHY  OP  SECONDARY  MECHANICAL  SCIENCES. 

repetition  of  the  first  spectrum,  and  is  mainly  useful  as  a 
standard  for  similar  phenomena,  and  not  for  colour  in 
general.  The  real  scale  of  colour  is  to  be  found,  as  we 
have  said,  in  the  numbers  which  express  the  thickness  of 
the  producing  film ; — in  the  length  of  a  fit  in  Newton's 
phraseology,  or  the  length  of  an  undulation  in  the  modern 
theory. 

7.  Scales  of  Impure  Colours. — The  standards  just  spoken 
of  include  (mainly  at  least)  only  pure  and  simple  colours ; 
and  however  complete  they  may  be  for  certain  objects  of 
the  science  of  op  tics,  they  are  insufficient  for  other  purposes. 
They  do  not  enable  us  to  put  in  their  place  mixed  and  im- 
pure colours.  And  there  is,  in  the  case  of  colour,  a  diffi- 
culty already  noticed,  which  does  not  occur  in  the  case  of 
sound ;  two  notes,  when  sounded  together,  are  not  neces- 
sarily heard  as  one ;  they  are  recognised  as  still  two,  and 
as  forming  a  concord  or  a  discord.  But  two  colours  form 
a  single  colour ;  and  the  eye  cannot,  in  any  way,  distin- 
guish between  a  green  compounded  of  blue  and  yellow, 
and  the  simple,  undecomposable  green  of  the  spectrum. 
By  composition  of  three  or  more  colours,  innumerable 
new  colours  may  be  generated  which  form  no  part  of  the 
prismatic  series ;  and  by  such  compositions  is  woven  the 
infinitely  varied  web  of  colour  which  forms  the  clothing 
of  nature.  How  are  we  to  classify  and  arrange  all  the 
possible  colours  of  objects,  so  that  each  shall  have  a  place 
and  name?  How  shall  we  find  a  chromatometer  for 
impure  as  well  as  for  pure  colour  ? 

Though  no  optical  investigations  have  depended  on  a 
scale  of  impure  colours,  such  a  scale  has  been  wanted  and 
invented  for  other  purposes ;  for  instance,  in  order  to 
identify  and  describe  objects  of  natural  history.  Not  to 
speak  of  earlier  essays,  we  may  notice  Werner's  Nomen- 
clature of  Colours,  devised  for  the  purpose  of  describing 
minerals.  This  scale  of  colour  was  far  superior  to  any 


MEASURE  OF  SECONDARY  QUALITIES.  317 

which  had  previously  been  promulgated.  It  was,  indeed, 
arbitrary  in  the  selection  of  its  degrees,  and  in  a  great 
measure  in  their  arrangement;  and  the  colours  were 
described  by  the  usual  terms,  though  generally  with  some 
added  distinction ;  as  blackish  green,  bluish  green,  apple 
green,  emerald  green.  But  the  great  merit  of  the  scale 
was  its  giving  a  fixed  conventional  meaning  to  these  terms, 
so  that  they  lost  much  of  their  usual  vagueness.  Thus 
apple-green  did  not  mean  the  colour  of  any  green  apple 
casually  taken ;  but  a  certain  definite  colour  which  the 
student  was  to  bear  in  mind,  whether  or  not  he  had  ever 
seen  an  apple  of  that  exact  hue.  The  words  were  not  a 
description,  but  a  record  of  the  colour :  the  memory  was 
to  retain  a  sensation,  not  a  name. 

The  imperfection  of  the  system  (arising  from  its  arbi- 
trary form)  was  its  incompleteness:  however  well  it 
served  for  the  reference  of  the  colours  which  it  did  con- 
tain, it  was  applicable  to  no  others ;  and  thus,  though 
Werner's  enumeration  extended  to  more  than  a  hundred 
colours,  there  occur  in  nature  a  still  greater  number 
which  cannot  be  exactly  described  by  means  of  it. 

In  such  cases  the  unclassed  colour  is,  by  the  Werne- 
rians,  defined  by  stating  it  as  intermediate  between  two 
others :  thus  we  have  an  object  described  as  between  eme- 
rald green  and  grass  green.  The  eye  is  capable  of  per- 
ceiving a  gradation  from  one  colour  to  another ;  such  as 
may  be  produced  by  a  gradual  mixture  in  various  ways. 
And  if  we  image  to  ourselves  such  a  mixture,  we  can 
compare  with  it  a  given  colour.  But  in  employing  this 
method  we  have  nothing  to  tell  us  in  what  part  of  the 
scale  we  must  seek  for  an  approximation  to  our  unclassed 
colour.  We  have  no  rule  for  discovering  where  we  are 
to  look  for  the  boundaries  of  the  definition  of  a  colour 
which  the  Wernerian  series  does  not  supply.  For  it  is 
not  always  between  contiguous  members  of  the  series 
that  the  undescribed  colour  is  found.  If  we  place  erne- 


318      PHILOSOPHY  OF  SECONDARY  MECHANICAL  SCIENCES. 

raid  green  between  apple  green  and  grass  green,  we  may 
yet  have  a  colour  intermediate  between  emerald  green 
and  leek  green ;  and,  in  fact,  the  Wernerian  series  of 
colours  is  destitute  of  a  principle  of  self-arrangement  and 
gradation;  and  is  thus  necessarily  and  incurably  imperfect. 

9.  We  should  have  a  complete  Scale  of  Colours,  if  we 
could  form  a  series  including  all  colours,  and  arranged  so 
that  each  colour  was  intermediate  in  its  tint  between  the 
adjacent  terms  of  the  series;  for  then,  whether  we  took 
many  or  few  of  the  steps  of  the  series  for  our  standard 
terms,  the  rest  could  be  supplied  by  the  law  of  continuity ; 
and  any  given  colour  would  either  correspond  to  one  of 
the  steps  of  our  scale  or  fall  between  two  intermediate 
ones.  The  invention  of  a  Chromatometer  for  Impure 
Colours,  therefore,  requires  that  we  should  be  able  to  form 
all  possible  colours  by  such  intermediation  in  a  systematic 
manner ;  that  is,  by  the  mixture  or  combination  of  cer- 
tain elementary  colours  according  to  a  simple  rule :  and 
we  are  led  to  ask  whether  such  a  process  has  been  shown 
to  be  possible. 

The  colours  of  the  prismatic  spectrum  obviously  do 
form  a  continuous  series ;  green  is  intermediate  between 
its  neighbours  yellow  and  blue,  orange  between  red  and 
yellow ;  and  if  we  suppose  the  two  ends  of  the  spectrum 
bent  round  to  meet  each  other,  so  that  the  arrangement 
of  the  colours  may  be  circular,  the  violet  and  indigo  will 
find  their  appropriate  place  between  the  blue  and  red. 
And  all  the  interjacent  tints  of  the  spectrum,  as  well  as 
the  ones  thus  named,  will  result  from  such  an  arrange- 
ment. Thus  all  the  pure  colours  are  produced  by  com- 
binations two  and  two  of  three  primary  colours,  red? 
yellow,  and  blue;  and  the  question  suggests  itself 
whether  these  three  are  not  really  the  only  primary 
colours,  and  whether  all  the  impure  colours  do  not  arise 
from  mixtures  of  the  three  in  various  proportions.  There 
are  various  modes  in  which  this  suggestion  may  be 


MEASURE  OF  SECONDARY  QUALITIES.  o!9 

applied  to  the  construction  of  a  scale  of  colours ;  but  the 
simplest  and  the  one  which  appears  really  to  verify  the  con- 
jecture that  all  possible  colours  may  be  so  exhibited,  is  the 
following.  A  certain  combination  of  red,  yellow,  and  blue, 
will  produce  black,  or  pure  grey,  and  when  diluted,  will 
give  all  the  shades  of  grey  which  intervene  between  black 
and  white.  By  adding  various  shades  of  grey,  then,,  to  pure 
colours,  we  may  obtain  all  the  possible  ternary  combina- 
tions of  red,  yellow,  and  blue ;  and  in  this  way  it  is  found 
that  we  exhaust  the  range  of  colours.  Thus  the  circle  of 
pure  colours  of  which  we  have  spoken  may  be  accompa- 
nied by  several  other  circles,  in  which  these  colours  are 
tinged  with  a  less  or  greater  shade  of  grey ;  and  in  this 
manner  it  is  found  that  we  have  a  perfect  chromatometer; 
every  possible  colour  being  exhibited  either  exactly  or  by 
means  of  approximate  and  contiguous  limits.  The  ar- 
rangement of  colours  has  been  brought  into  this  final  and 
complete  form  by  M.  Merimee,  whose  chromatic  scale  is 
published  by  M.  Mirbel  in  his  Elements  of  Botany.  We  may 
observe  that  such  a  standard  affords  us  a  numerical  expo- 
nent for  every  colour  by  means  of  the  proportions  of  the 
three  primary  colours  which  compose  it ;  or,  expressing 
the  same  result  otherwise,  by  means  of  the  pure  colour 
which  is  involved,  and  the  proportion  of  grey  by  which 
it  is  rendered  impure.  In  such  a  scale  the  fundamental 
elements  would  be  the  precise  tints  of  red,  yellow,  and 
blue  which  are  found  or  assumed  to  be  primary;  the 
numerical  exponents  of  each  colour  would  depend  upon 
the  arbitrary  number  of  degrees  which  we  interpose  be- 
tween each  two  primary  colours ;  and  between  each  pure 
colour  and  absolute  blackness.  No  such  numerical 
scale  has,  however,  as  yet,  obtained  general  acceptation. 

10.  (III.)  Scales  of  Light.  Photometer. — Another  instru- 
ment much  needed  in  optical  researches  is  a  Photometer,  a 
measure  of  the  intensity  of  light.  In  this  case,  also, 
the  organ  of  sense,  the  eye,  is  the  ultimate  judge ;  nor 


320      PHILOSOPHY  OF  SECONDARY  MECHANICAL  SCIENCES. 

has  any  effect  of  light,  as  light,  yet  been  discovered  which 
we  can  substitute  for  such  a  judgment.     All  instruments, 
such  as  that  of  Leslie,  which  employ  the  heating  effect  of 
light,  or  at  least  all  that  have  hitherto  been  proposed,  are  in- 
admissible as  photometers.    But  though  the  eye  can  judge 
of  two  surfaces  illuminated  by  light  of  the  same  colour, 
and  can  determine  when  they  are  equally  bright,  or  which 
is  the  brighter,  the   eye   can  by  no  means  decide  at  sight 
the   proportion   of    illumination.      How  much    in   such 
judgments  we  are  affected  by  contrast,  is  easily  seen  when 
we  consider  how  different  is  the  apparent  brightness  of 
the  moon  at  mid-day  and  at  midnight,  though   the  light 
which  we  receive  from  her  is,  in  fact,  the  same  at  both 
periods.     In  order  to  apply  a  scale  in  this  case,  we  must 
take  advantage  of  the  known  numerical  relations  of  light. 
We  are  certain  that  if  all  other  illumination  be  excluded, 
two  equal  luminaries,  under  the  same  circumstances,  will 
produce  an  illumination  twice  as  great  as  one  does ;  and 
we  can  easily  prove,  from  mathematical  considerations, 
that   if  light  be  not  enfeebled  by  the  medium  through 
which   it   passes,  the  illumination  on    a   given   surface 
will  diminish  as  the  square  of  the  distance  of  the  lumi- 
nary increases.     If,  therefore,  we  can  by  taking  a  frac- 
tion thus  known  of  the  illuminating  effect  of  one  lumi- 
nary, make  it  equal  to  the  total  effect  of  another,  of  which 
equality  the  eye  is  a  competent  judge,  we  compare  the 
effects  of  the   two  luminaries.     In  order  to  make   this 
comparison  we  may,  with  Rumford,  look  at  the  shadows 
of  the  same   object  made   by  the  two   lights,    or  with 
Ritchie,  we  may  view  the  brightness  produced  on  two 
contiguous  surfaces,  framing  an  apparatus    so  that  the 
equality  may  be  brought  about  by  proper  adjustment ;  and 
thus  a  measure  will  become  practicable.     Or  we  may  em- 
ploy other  methods  as  was  done  by  Wollaston*,  who 
reduced  the  light  of  the  sun  by  observing  it  as  reflected 
*  Phil.  Trans.,  1829,  p.  19. 


MEASURE  OF  SECONDARY  QUALITIES.  o21 

from  a  bright  globule,  and  thus  found  the  light  of  the 
sun  to  be  10,000,000,000  times  that  of  Sirius,  the 
brightest  fixed  star.  All  these  methods  are  inaccurate, 
even  as  methods  of  comparison ;  and  do  not  offer  any 
fixed  or  convenient  numerical  standard ;  but  none  better 
have  yet  been  devised. 

10.  Cyanometer. — As  we  thus  measure  the  brightness 
of  a  colourless  light,  we  may  measure  the  intensity  of  any 
particular  colour  in  the  same  way ;  that  is,  by  applying 
a  standard   exhibiting  the  gradations  of  the  colour  in 
question  till  we  find  a  shade  which  is  seen  to  agree  with 
the  proposed  object.     Such  an  instrument  we  have  in  the 
Cyanometer,  which  was   invented   by   Saussure   for   the 
purpose  of  measuring  the  intensity  of  the  blue  colour  of 
the  sky.     We  may  introduce  into  such  an  instrument  a 
numerical  scale,  but  the  numbers  in  such  a  scale  will  be 
altogether  arbitrary. 

11.  (IV.)  Scales  of  Heat. — When  we  proceed  to  the 
sensation  of  heat,  and  seek  a  measure  of  that  quality,  we 
find,  at  first  sight,  new  difficulties.     Our  sensations  of  this 
kind  are  more  fluctuating  than  those  of  vision ;  for  we 
know  that  the  same  object  may  feel  warm  to  one  hand 
and  cold  to  another  at  the  same  instant,  if  the  hands 
have  been  previously  cooled  and  warmed   respectively. 
Nor  can  we  obtain  here,  as  in  the  case  of  light,  self-evi- 
dent numerical  relations  of  the  heat  communicated  in 
given  circumstances ;  for  we  know  that  the  effect  so  pro- 
duced will  depend  on  the  warmth  of  the  body  to  be 
heated,  as  well  as  on  that  of  the  source  of  heat;  the 
summer  sun,  which  warms  our  bodies,  will  not  augment 
the  heat    of  a  red-hot  iron.     The  cause    of  the   diffe- 
rence of  these  cases  is,  that  bodies  do  not  receive  the 
whole  of  their  heat,  as  they  receive  the  whole  of  their 
light,  from  the  immediate  influence  of  obvious  external 
agents.     There   is   no  readily-discovered  absolute  cold, 

VOL.  I.  Y 


322       PHILOSOPHY  OF  SECONDARY  MECHANICAL  SCIENCES. 

corresponding  to  the  absolute  darkness  which  we  can  easily 
produce  or  imagine.  Hence  we  should  be  greatly  at  a 
loss  to  devise  a  Thermometer,  if  we  did  not  find  an  indirect 
effect  of  heat  sufficiently  constant  and  measurable  to 
answer  this  purpose.  We  discover,  however,  such  an 
effect  in  the  expansion  of  bodies  by  the  effect  of  heat. 

12.  Many  obvious  phenomena  show  that  air,  under 
given  circumstances,  expands  by  the  effect  of  heat ;  the 
same  is  seen  to  be  true  of  liquids,  as  of  water,  and  spirit 
of  wine ;  and  the  property  is  found  to  belong  also  to  the 
metallic  fluid,  quicksilver.     A  more  careful  examination 
showed  that  the  increase  of  bulk  in  some  of  these  bodies 
by  increase  of  heat  was  a  fact  of  a  nature  sufficiently  con- 
stant and  regular  to  afford  a  means  of  measuring  that 
previously  intangible  quality ;  and  the  Thermometer  was 
invented.     There    were,    however,    many  difficulties    to 
overcome,  and  many  points  to  settle  before  this  instru- 
ment was  fit  for  the  purposes  of  science. 

An  explanation  of  the  way  in  which  this  was  done 
necessarily  includes  an  important  chapter  of  the  history 
of  Thermotics.  We  must  now,  therefore,  briefly  notice 
historically  the  progress  of  the  Thermometer.  The  lead- 
ing steps  of  this  progress,  after  the  first  invention  of  the 
instrument,  were — The  establishment  of  fixed  points  in 
the  thermometric  scale— The  comparison  of  the  scales  of 
different  substances — And  the  reconcilement  of  these 
differences  by  some  method  of  interpreting  them  as  indi- 
cations of  the  absolute  quantity  of  heat. 

13.  It  would  occupy  too  much  space  to  give  in  detail 
the  history  of  the  successive  attempts  by  which  these  steps 
were  effected.     A  thermometer   is   described   by  Bacon 
under  the  title  Vitrum  Calendare ;  this  was  an  air  ther- 
mometer.    Newton  used  a  thermometer  of  linseed  oil, 
and  he  perceived  that  the  first  step  requisite   to  give 
value  to  such  an  instrument  was  to  fix  its  scale ;  accord- 


MEASURE  OF  SECONDARY  QUALITIES.  823 

ingly  he  proposed  his  Scala  Graduum  Caloris*.  But 
when  thermometers  of  different  liquids  were  compared, 
it  appeared,  from  their  discrepancies,  that  this  fixation  of 
the  scale  of  heat  was  more  difficult  than  had  been  sup- 
posed. It  was,  however,  effected.  Newton  had  taken 
freezing  water,  or  rather  thawing  snow,  as  the  zero  of  his 
scale,  which  is  really  a  fixed  point ;  Halley  and  Amontons 
discovered  (in  1693  and  1702)  that  the  heat  of  boiling 
water  is  another  fixed  point ;  and  Daniel  Gabriel  Fahren- 
heit, of  Dantzig,  by  carefully  applying  these  two  standard 
points,  produced,  about  1714,  thermometers,  which  were 
constantly  consistent  with  each  other.  This  result  was 
much  admired  at  the  time,  and  was,  in  fact,  the  solution 
of  the  problem  just  stated,  the  fixation  of  the  scale  of  heat. 

14.  But  the  scale  thus  obtained  is  a  conventional  not 
a  natural  scale.     It  depends  upon  the  fluid  employed  for 
the  thermometer.     The  progress  of  expansion  from  the 
heat  of  freezing  to  that  of  boiling  water  is  different  for 
mercury,  oil,  water,  spirit  of  wine,  air.     A  degree  of  heat 
which  is   half-way  between   these  two  standard  points 
according  to  a  mercurial  thermometer,  will  be  below  the 
half-way  point  in  a  spirit  thermometer,  and  above  it  in 
an  air  thermometer.     Each  liquid  has  its  own  march  in 
the  course  of  its  expansion.     Deluc  and  others  compared 
the  marches  of  various  liquids,  and  thus  made  what  we 
may  call  a  concordance  of  thermometers  of  various  kinds. 

15.  Here  the  question  farther  occurs:  Is  there  not 
some  natural  measure  of  the  degrees  of  heat  ?     It  appears 
certain  that  there  must  be  such  a  measure,  and  that  by 
means  of  it  all  the  scales  of  different  liquids  must  be 
reconciled.     Yet  this  does  not  seem  to  have  occurred  at 
once  to   men's  minds.     Deluc,  in   speaking   of  the  re- 
searches which  we  have  just  mentioned,  saysf ,  "  When  I 
undertook  these  experiments,  it  never  once  came  into  my 

*  Phil.  Trans.,  1701.          t  Modif.  de  HAtmosph.,  1782,  p.  303. 

Y  2 


324      PHILOSOPHY  OF  SECONDARY  MECHANICAL  SCIENCES. 

thoughts  that  they  could  conduct  me  with  any  probability 
to  a  table  of  real  degrees  of  heat  But  hope  grows  with 
success,  and  desire  with  hope."  Accordingly  he  pursued 
this  inquiry  for  a  long  course  of  years. 

What  are  the  principles    by  which   we   are  to    be 
guided  to  the  true  measure  of  heat  ?     Here,  as  in  all  the 
sciences  of  this  class,  we  have  the  general  principle,  that 
the  secondary  quality,  heat,  must  be  supposed  to  be  per- 
ceived in  some  way  by  a  material  medium  or  fluid.     If 
we  take  that  which  is,  perhaps,  the  simplest  form  of  this 
hypothesis,  that  the  heat  depends  upon  the  quantity  of  this 
fluid,  or  caloric,  which  is  present,  we  shall  find  that  we  are 
led  to  propositions  which  may  serve  as  a  foundation  for  a 
natural  measure  of  heat.     The  Method  of  Mixtures   is 
one  example  of  such  a  result.     If  we  mix  together  two 
pints  of  water,  one  hot  and  one  cold,  is  it  not  manifest 
that  the  temperature  of  the  mixture  must  be  midway 
between  the  two  ?    Each  of  the  two  portions  brings  with  it 
its  own  heat,     The  whole  heat,  or  caloric,  of  the  mixture 
is  the  sum  of  the  two  ;  and  the  heat  of  each  half  must  be 
the  half  of  this  sum,  and  therefore  its  temperature  must 
be  intermediate  between  the  temperatures  of  the  equal 
portions  which  were  mixed.      Deluc  made  experiments 
founded  upon  this  principle,  and  was  led  by  them  to  con- 
clude that  "  the  dilatations  of  mercury  follow  an  accele- 
rated march  for  successive  equal  augmentations  of  heat." 

But  there  are  various  circumstances  which  prevent 
this  method  of  mixtures  from  being  so  satisfactory  as  at 
first  sight  it  seems  to  promise  to  be.  The  different  capa- 
cities for  heat  of  different  substances,  and  even  of  the 
same  substance  at  different  temperatures,  introduce  much 
difficulty  into  the  experiments,  and  this  path  of  inquiry 
has  not  yet  led  to  a  satisfactory  result. 

16.  Another  mode  of  inquiring  into  the  natural  measure 
of  heat  is  to  seek  it  by  researches  on  the  law  of  cooling  of 


MEASURE  OF  SECONDARY  QUALITIES.  325 

hot  bodies.  If  we  assume  that  the  process  of  cooling  of 
hot  bodies  consists  in  a  certain  material  heat  flying  off, 
we  may,  by  means  of  certain  probable  hypotheses,  deter- 
mine mathematically  the  law  according  to  which  the  tem- 
perature decreases  as  time  goes  on ;  and  we  may  assume 
that  to  be  the  true  measure  of  temperature  which  gives 
to  the  experimental  law  of  cooling  the  most  simple  and 
probable  form. 

It  appears  evident  from  the  most  obvious  conceptions 
which  we  can  form  of  the  manner  in  which  a  body  parts 
with  its  superabundant  heat,  that  the  hotter  a  body  is,  the 
faster  it  cools ;  though  it  is  not  clear  without  experi- 
ment, by  what  law  the  rate  of  cooling  will  depend  upon 
the  heat  of  the  body.  Newton  took  for  granted  the  most 
simple  and  seemingly  natural  law  of  this  dependence :  he 
supposed  the  rate  of  cooling  to  be  proportional  to  the 
temperature,  and  from  this  supposition  he  could  deduce 
the  temperature  of  a  hot  iron,  calculating  from  the  original 
temperature  and  the  time  during  which  it  had  been  cool- 
ing. By  calculation  founded  on  such  a  basis,  he  graduated 
his  thermometer. 

17.  But  a  little  further  consideration  showed  that  the 
rate  of  cooling  of  hot  bodies  depended  upon  the  tempera- 
ture of  the  surrounding  bodies,  as  well  as  upon  its  own 
temperature.  Prevost's  Theory  of  Exchanges*  was  pro- 
pounded with  a  view  of  explaining  this  dependence,  and 
was  generally  accepted.  According  to  this  theory,  all 
bodies  radiate  heat  to  one  another,  and  are  thus  con- 
stantly giving  and  receiving  heat ;  and  a  body  which  is 
hotter  than  surrounding  bodies,  cools  itself,  and  warms 
the  surrounding  bodies,  by  an  exchange  of  heat  for  heat, 
in  which  they  are  the  gainers.  Hence  if  0  be  the  tem- 
perature of  the  bodies,  or  of  the  space,  by  which  the  hot 
body  is  surrounded,  and  0  +  t  the  temperature  of  the  hot 

*  Recherche*  sur  la  Chaleur,  1791.     Hist,  Ind.  #«'.,  ii.  474. 


326      PHILOSOPHY  OF  SECONDARY  MECHANICAL  SCIENCES. 

body,  the  rate  of  cooling  will  depend  upon  the  excess  of 
the  radiation  for  a  temperature  0  +  t,  above  the  radiation 
for  a  temperature  0. 

Accordingly,  in  the  admirable  researches  of  MM. 
Dulong  and  Petit  upon  the  cooling  of  bodies,  it  was 
assumed  that  the  rate  of  cooling  of  the  hot  body  was 
represented  by  the  excess  of  F(0-M)  above  F(#);  where 
F  represented  some  mathematical  function,  that  is,  some 
expression  obtained  by  arithmetical  operations  from  the 
temperatures  6  + 1  and  0  ;  although  what  these  operations 
are  to  be,  was  left  undecided,  and  was  in  fact  determined 
by  the  experiments.  And  the  result  of  their  investiga- 
tions was,  that  the  function  is  of  this  kind  :  when  the 
temperature  increases  by  equal  intervals,  the  function 
increases  in  a  continued  geometric  proportion*.  This 
was,  in  fact,  the  same  law  which  had  been  assumed  by 
Newton  and  others,  with  •this  difference,  that  they  had 
neglected  the  term  which  depends  upon  the  temperature 
of  the  surrounding  space. 

18.  This  law  falls  in  so  well  with  the  best  conceptions 
we  can  form  of  the  mechanism  of  cooling  upon  the  suppo- 
sition of  a  radiant  fluid  caloric,  that  it  gives  great  proba- 
bility to  the  scale  of  temperature  on  which  the  simplicity 
of  the  result  depends.  Now  the  temperatures  in  the 
formulae  just  referred  to  were  expressed  by  means  of.  the 
air  thermometer.  Hence  MM.  Dulong  and  Petit  justly 
state  that  while  all  different  substances  employed  as  ther- 
mometers give  different  laws  of  thermotical  phenomena, 
their  own  success  in  obtaining  simple  and  general  laws 
by  means  of  the  air  thermometer,  is  a  strong  recommen- 
dation of  that  as  the  natural  scale  of  heat.  They  add  f, 

H  t  9 

*  The  formula  for  the  rate  of  cooling  is  ma          —  ma  ,  where  the 

quantity  m   depends  upon  the  nature   of  the    body,  the  state  of  it 
surface,  and  other  circumstances. — Ann.  Ckim.  vii.  150. 
t  Annales  de  Ckimie,  \ii.  153. 


MEASURE  OF  SECONDARY  QUALITIES.  327 

'*  The  well-known  uniformity  of  the  principal  physical 
properties  of  all  gases,  and  especially  the  perfect  identity 
of  their  laws  of  dilatation  by  heat,  [a  very  important 
discovery  of  Dalton  and  Gay  Lussac*,]  make  it  very 
probable  that  in  this  class  of  bodies  the  disturbing  causes 
have  not  the  same  influence  as  in  solids  and  liquids ;  and 
consequently  that  the  changes  of  bulk  produced  by  the 
action  of  heat  are  here  in  a  more  immediate  dependence 
on  the  force  which  produces  them." 

19.  Still  we  cannot  consider  this  point  as  settled 
till  we  obtain  a  more  complete  theoretical  insight  into 
the  nature  of  heat  itself.  If  it  be  true  that  heat  con- 
sists in  the  vibrations  of  a  fluid,  then,  although,  as 
Ampere  has  shown f,  the  laws  of  radiation  will,  on 
mathematical  grounds,  be  the  same  as  they  are  on  the 
hypothesis  of  emission,  we  cannot  consider  the  natural 
scale  of  heat  as  determined,  till  we  have  discovered 
some  means  of  measuring  the  caloriferous  vibrations 
as  we  measure  luminiferous  vibrations.  We  shall  only 
know  what  the  quantity  of  heat  is  when  we  know  what 
heat  itself  is  ; — when  we  have  obtained  a  theory  which 
satisfactorily  explains  the  manner  in  which  the  sub- 
stance or  medium  of  heat  produces  its  effects.  When 
we  see  how  radiation  and  conduction,  dilatation  and 
liquefaction  are  all  produced  by  mechanical  changes  of 
the  same  fluid,  we  shall  then  see  what  the  nature  of  that 
change  is  which  dilatation  really  measures,  and  what 
relation  it  bears  to  any  more  proper  standard  of  heat. 

We  may  add,  that  while  our  thermotical  theory  is 
still  so  imperfect  as  it  is,  all  attempts  to  divine  the  true 
nature  of  the  relation  between  light  and  heat  are  pre- 
mature, and  must  be  in  the  highest  degree  insecure  and 
visionary.  Speculations  in  which,  from  the  general 
assumption  of  a  caloriferous  and  luminiferous  medium, 

*  ffist.  Ind.  $».,  ii.,  496.  f  //>.,  ii.,  528. 


328       PHILOSOPHY  OF  SECONDARY  MECHANICAL  SCIENCES. 

and  from  a  few  facts  arbitrarily  selected  and  loosely 
analysed,  a  general  theory  of  light  and  heat  is  asserted, 
are  entirely  foreign  to  the  course  of  inductive  science, 
and  cannot  lead  to  any  stable  and  substantial  truth. 

20.  Other  Instruments  for  measuring  Heat. — It  does  not 
belong  to  our  present  purpose  to  speak  of  instruments  of 
which  the  object  is  to  measure,  not  sensible  qualities,  but 
some  effect  or  modification  of  the  cause  by  which  such 
qualities  are  produced :  such,  for  instance,  are  the  Calo- 
rimeter, employed  by  Lavoisier  and  Laplace,  in  order  to 
compare  the  specific  heat  of  different  substances  ;  and 
the  Actinometer,  invented  by  Sir  John  Herschel,  in  order 
to  determine  the  effect  of  the  sun's  rays  by  means  of  the 
heat  which  they  communicate  in  a  given  time ;  which 
effect  is,  as  may  readily  be  supposed,  very  different  under 
different  circumstances  of  atmosphere  and  position.  The 
laws  of  such  effects  may  be  valuable  contributions  to  our 
knowledge  of  heat,  but  the  interpretation  of  them  must 
depend  on  a  previous  knowledge  of  the  relations  which 
temperature  bears  to  heat,  according  to  the  views  just 
explained. 

21.  (V.)   Scales  of  other  Qualities. — Before  quitting 
the  subject  of  the  measures  of  sensible  qualities,  we  may 
observe  that  there  are  several  other  such  qualities  for 
which  it  would  be  necessary  to  have  scales  and  means  of 
measuring,  in  order  to  make  any  approach  to  science  on 
such  subjects.     This  is  true,  for  instance,  of  tastes  and 
smells.     Indeed  some  attempts  have  been  made  towards 
a  classification  of  the  tastes  of  sapid  substances,  but  these 
have   not   yet   assumed   any   satisfactory   or   systematic 
character;   and  I  am  not  aware  that  any  instruments 
have  been  suggested  for  measuring  either  the  flavour  or 
the  odour  of  bodies  which  possess  such  qualities. 

22.  Quality  of  Sounds. — The  same  is  true  of  that  kind 
of  difference  in  sounds  which  is  peculiarly  termed  their 


MEASURE  OF  SECONDARY  QUALITIES.  329 

quality;  that  character  by  which,  for  instance,  the  sound 
of  a  flute  differs  from  that  of  a  hautbois,  when  the  note 
is  the  same ;  or  a  woman's  voice  from  a  boy's. 

23.  Articulate  Sounds. — There  is  also  in  sounds  another 
difference,  of  which  the  nature  is  still  obscure,  but  in 
reducing  which  to  rule,  and  consequently  to  measure, 
some  progress  has  nevertheless  been  made.  I  speak  of 
the  differences  of  sound  considered  as  articulate.  Classi- 
fications of  the  sounds  of  the  usual  alphabets  have  been 
frequently  proposed ;  for  instance,  that  which  arranges 
the  consonants  into  the  following  groups  : — 

Sharp.  Flat.  Sharp  Aspirate.  Flat  Aspirate.  Nasal. 

p                 b  ph  (/)                  bh  (v)  m 

k                g  (hard)  kh                          gh  ng 

t                d  th  (sharp)           th  (flat)  n 

s                z  sh                         zh 

It  is  easily  perceived  that  the  relations  of  the  sounds  in 
each  of  these  horizontal  lines  are  analogous ;  and  accord- 
ingly the  rules  of  derivation  and  modification  of  words 
in  several  languages  proceed  upon  such  analogies.  In 
the  same  manner  the  vowels  may  be  arranged  in  an  order 
depending  on  their  sound.  But  to  make  such  arrange- 
ments fixed  and  indisputable,  we  ought  to  know  the 
mechanism  by  which  such  modifications  are  caused. 
Instruments  have  been  invented  by  which  some  of  these 
sounds  can  be  imitated ;  and  if  such  instruments  could 
be  made  to  produce  the  above  series  of  articulate  sounds, 
by  connected  and  regular  processes,  we  should  find,  in  the 
process,  a  measure  of  the  sound  produced.  This  has  been 
in  a  great  degree  effected  for  the  Vowels  by  Professor 
Willis's  artificial  mode  of  imitating  them.  For  he  finds 
that  if  a  musical  reed  be  made  to  sound  through  a  cylin- 
drical pipe,  we  obtain  by  gradually  lengthening  the  cylin- 
drical pipe,  the  series  of  vowels  i,  E,  A,  o,  u,  with 
intermediate  sounds*.  In  this  instrument,  then,  the 
*  Camb.  Trans.,  vol.  iii.,  p.  239. 


330      PHILOSOPHY  OF  SECONDARY  MECHANICAL  SCIENCES. 

length  of  the  pipe  would  determine  the  vowel,  and 
might  be  used  numerically  to  express  it.  Such  an 
instrument  so  employed  would  be  a  measure  of  vowel 
quality. 

Our  business  at  present,  however,  is  not  with  instru- 
ments which  might  be  devised  for  measuring  sensible 
qualities,  but  with  those  which  have  been  so  used,  and 
have  thus  been  the  basis  of  the  sciences  in  which  such 
qualities  are  treated  of;  and  this  we  have  now  done  suf- 
ficiently for  our  present  purpose. 

24.  There  is  another  Idea  which,  though  hitherto  very 
vaguely  entertained,  has  had  considerable  influence  in  the 
formation,  both  of  the  sciences  spoken  of  in  the  present 
Book,  and  on  others  which  will  hereafter  come  under  our 
notice:  namely,  the  Idea  of  Polarity.  This  Idea  will  be 
the  subject  of  the  ensuing  Book.  And  although  this 
Idea  forms  a  part  of  the  basis  of  various  other  extensive 
portions  of  science,  as  Optics  and  Chemistry,  it  occupies 
so  peculiarly  conspicuous  a  place  in  speculations  belong- 
ing to  what  I  have  termed  the  Mechanico-Chemical 
Sciences,  (Magnetism  and  Electricity,)  that  I  shall  desig- 
nate the  discussion  of  the  Idea  of  Polarity  as  the  Philo- 
sophy of  those  Sciences. 


331 


BOOK   V. 


OF  THE  PHILOSOPHY  OF  THE  MECHANICO- 
CHEMICAL  SCIENCES. 


CHAPTER  I. 

ATTEMPTS  AT   THE   SCIENTIFIC  APPLICATION 
OF  THE  IDEA  OF  POLARITY. 

1 .  IN  some  of  the  mechanical  sciences,  as  Magnetism 
and  Optics,  the  phenomena  are  found  to  depend  upon  posi- 
tion (the  position  of  the  magnet,  or  of  the  ray  of  light,) 
in  a  peculiar  alternate  manner.  This  dependence,  as  it 
was  first  apprehended,  was  represented  by  means  of 
certain  conceptions  of  space  and  force,  as  for  instance  by 
considering  the  two  poles  of  a  magnet.  But  in  all  such 
modes  of  representing  these  alternations  by  the  concep- 
tions borrowed  from  other  ideas,  a  closer  examination 
detected  something  superfluous  and  something  defective  ; 
and  in  proportion  as  the  view  which  philosophers  took  of 
this  relation  was  gradually  purified  from  these  incongru- 
ous elements,  and  was  rendered  more  general  and  abstract 
by  the  discovery  of  analogous  properties  in  new  cases,  it 
was  perceived  that  the  relation  could  not  be  adequately 
apprehended  without  considering  it  as  involving  a 
peculiar  and  independent  Idea,  which  we  may  designate 
by  the  term  Polarity. 

We  shall  trace  some  of  the  forms  in  which  this  Idea 
has  manifested  itself  in  the  history  of  science.  In  doing 
so  we  shall  not  begin,  as  in  other  Books  of  this  work 


332     PHILOSOPHY  OF  THE  MECHANICO-CHEMICAL  SCIENCES. 

we  have  done,  by  speaking  of  the  notion  as  it  is  employed 
in  common  use:  for  the  relation  of  polarity  is  of  so 
abstract  and  technical  a  nature,  that  it  is  not  employed, 
at  least  in  any  distinct  and  obvious  manner,  on  any 
ordinary  or  practical  occasions.  The  idea  belongs  pecu- 
liarly to  the  region  of  speculation :  in  persons  of  com- 
mon habits  of  thought  it  is  probably  almost  or  quite 
undeveloped  ;  and  even  most  of  those  whose  minds  have 
been  long  occupied  by  science,  find  a  difficulty  in  appre- 
hending it  in  its  full  generality  and  abstraction,  and  stript 
of  all  irrelevant  hypothesis. 

2.  Magnetism. — The  name  and  the  notion  of  Poles 
were  first  adopted  in  the  case  of  a  magnet.  If  we  have 
two  magnets,  their  extremities  attract  and  repel  each 
other  alternatively.  If  the  first  end  of  the  one  attract 
the  first  end  of  the  other,  it  repels  the  second  end,  and 
conversely.  In  order  to  express  this  rule  conveniently, 
the  two  ends  of  each  magnet  are  called  the  north  pole  and 
the  south  pole  respectively,  the  denominations  being  bor- 
rowed from  the  poles  of  the  earth  and  heavens.  "  These 
poles,"  as  Gilbert  says*,  "regulate  the  motions  of  the 
celestial  spheres  and  of  the  earth.  In  like  manner  the 
magnet  has  its  poles,  a  northern  and  a  southern  one ; 
certain  and  determined  points  constituted  by  nature  in 
the  stone,  the  primary  terms  of  its  motions  and  effects, 
the  limits  and  governors  of  many  actions  and  virtues." 

The  nature  of  the  opposition  of  properties  of  which 
we  speak  may  be  stated  thus. 

The  North  pole  of  one  magnet  attracts  the  South 
pole  of  another  magnet. 

The  North  pole  of  one  magnet  repels  the  North  pole 
of  another  magnet. 

The  South  pole  of  one  magnet  repels  the  South  pole 
of  another  magnet. 

*  De  Magn.,  lib.  i.  c.  3. 


APPLICATION  OF  THE  IDEA  OF  POLARITY.  333 

The  South  pole  of  one  magnet  attracts  the  North 
pole  of  another  magnet. 

It  will  be  observed  that  the  contrariety  of  position 
which  is  indicated  by  putting  the  South  pole  for  the  North 
pole  in  either  magnet,  is  accompanied  by  the  opposition 
of  mechanical  effect  which  is  expressed  by  changing 
attraction  into  repulsion  and  repulsion  into  attraction: 
and  thus  we  have  the  general  feature  of  polarity: — A 
contrast  of  properties  corresponding  to  a  contrast  of 
positions. 

3.  Electricity. — When  the  phenomena  of  electricity 
came  to  be  studied,  it  appeared  that  they  involved  rela- 
tions in  some  respects  analogous  to  those  of  magnetism. 

Two  kinds  of  electricity  were  distinguished,  the 
positive  and  the  negative;  arid  it  appeared  that  two 
bodies  electrized  positively  or  two  electrized  negatively, 
repelled  each  other,  like  two  north  or  two  south  magnetic 
poles ;  while  a  positively  and  a  negatively  electrized  body 
attracted  each  other,  like  the  north  and  south  poles  of 
two  magnets.  In  conductors  of  an  oblong  form,  the 
electricity  could  easily  be  made  to  distribute  itself  so 
that  one  end  should  be  positively  and  one  end  negatively 
electrized ;  and  then  such  conductors  acted  on  each  other 
exactly  as  magnets  would  do. 

But  in  conductors,  however  electrized,  there  is  no 
peculiar  point  which  can  permanently  be  considered  as 
the  pole.  The  distribution  of  electricity  in  the  conduc- 
tor depends  upon  external  circumstances :  and  thus, 
although  the  phenomena  offer  the  general  character  of 
polarity — alternative  results  corresponding  to  alternative 
positions, — they  cannot  be  referred  to  poles.  Some  other 
mode  of  representing  the  forces  must  be  adopted  than 
that  which  makes  them  emanate  from  permanent  points 
as  in  a  magnet. 

The  phenomena  of  attraction  and  repulsion  in  elec- 


334     PHILOSOPHY  OF  THE  MECHANICO-CHEMICAL  SCIENCES. 

trized  bodies  were  conveniently  represented  by  means  of 
the  hypothesis  of  two  electric  fluids^  a  positive  and  a 
negative  one,  which  were  supposed  to  be  distributed  in 
the  bodies.  Of  these  fluids,  it  was  supposed  that  each 
repelled  its  own  parts  and  attracted  those  of  the  opposite 
fluid :  and  it  was  found  that  this  hypothesis  explained  all 
the  obvious  laws  of  electric  action.  Here  then  we  have 
the  phenomena  of  polarization  explained  by  a  new  kind 
of  machinery : — two  opposite  fluids  distributed  in  bodies, 
and  supplying  them,  so  to  speak,  with  their  polar  forces. 
This  hypothesis  not  only  explains  electrical  attraction, 
but  also  the  electrical  spark :  when  two  bodies,  of  which 
the  neighbouring  surfaces  are  charged  with  the  two 
opposite  fluids,  approach  near  to  each  other,  the  mutual 
attraction  of  the  fluids  becomes  more  and  more  intense, 
till  at  last  the  excess  of  fluid  on  the  one  body  breaks 
through  the  air  and  rushes  to  the  other  body,  in  a  form 
accompanied  by  light  and  noise.  When  this  transfer  has 
taken  place,  the  attraction  ceases,  the  positive  and  the 
negative  fluid  having  neutralized  each  other.  Their 
effort  was  to  unite  ;  and  this  union  being  effected,  there 
is  no  longer  any  force  in  action.  Bodies  in  their  natural 
unexcited  condition  may  be  considered  as  occupied  by  a 
combination  of  the  two  fluids :  and  hence  we  see  how 
the  production  of  either  kind  of  electricity  is  necessarily 
accompanied  with  the  production  of  an  equivalent  amount 
of  the  opposite  kind. 

4.  Voltaic  Electricity. — Such  is  the  case  in  Franklinic 
electricity, — that  which  is  excited  by  the  common  elec- 
trical machine.  In  studying  Voltaic  electricity,  we  are 
led  to  the  conviction  that  the  fluid  which  is  in  a  condition 
of  momentary  equilibrium  in  electrized  conductors,  exists 
in  the  state  of  current  in  the  voltaic  circuit.  And  here 
we  find  polar  relations  of  a  new  kind  existing  among 
the  forces.  Two  voltaic  currents  attract  each  other  when 


APPLICATION  OF  THE  IDEA  OF  POLARITY.  335 

they  are  moving  in  the  same,  and  repel  each  other  when 
they  are  moving  in  opposite,  directions. 

But  we  find,  in  addition  to  these,  other  polar  relations 
of  a  more  abstruse  kind,  and  which  the  supposition  of 
two  fluids  does  not  so  readily  explain.  For  instance,  if 
such  fluids  existed,  distinct  from  each  other,  it  might 
be  expected  that  it  would  be  possible  to  exhibit  one 
of  them  separate  from  the  other.  Yet  in  all  the  phe- 
nomena of  electromotive  currents,  we  attempt  in  vain 
to  obtain  one  kind  of  electricity  separately.  "  I  have 
not,"  says  Mr.  Faraday*,  "been  able  to  find  a  single 
fact  which  could  be  adduced  to  prove  the  theory  of 
two  electricities  rather  than  one,  in  electric  currents ; 
or,  admitting  the  hypothesis  of  two  electricities,  have 
I  been  able  to  perceive  the  slightest  grounds  that  one 
electricity  can  be  more  powerful  than  the  other, — or 
that  it  can  be  present  without  the  other, — or  that  it 
can  be  varied  or  in  the  slightest  degree  affected  without 
a  corresponding  variation  in  the  other."  "Thus,"  he 
adds,  "  the  polar  character  of  the  powers  is  rigorous  and 
complete."  Thus,  we  too  may  remark,  all  the  super- 
fluous and  precarious  parts  gradually  drop  off  from  the 
hypothesis  which  we  devise  in  order  to  represent  polar 
phenomena ;  and  the  abstract  notion  of  polarity — of  equal 
and  opposite  powers  called  into  existence  by  a  com- 
mon condition — remains  unincumbered  with  extraneous 
machinery. 

5.  Light. — Another  very  important  example  of  the 
application  of  the  idea  of  polarity  is  that  supplied  by  the 
discovery  of  the  polarization  of  light.  A  ray  of  light 
may,  by  various  processes,  be  modified,  so  that  it  has  dif- 
ferent properties  according  to  its  different  sides,  although 
this  difference  is  not  perceptible  by  any  common  effects. 
If,  for  instance,  a  ray  thus  modified,  pass  perpendicularly 

*  Researches,  516. 


336    PHILOSOPHY  OF  THE  MECHANICO-CHEMICAL  SCIENCES. 

through  a  circular  glass,  and  fall  upon  the  eye,  we  may 
turn  the  glass  round  and  round  its  frame,  and  we  shall 
make  no  difference  in  the  brightness  of  the  spot  which 
we  see.     But  if,  instead  of  a  glass,  we  look  through  a 
longitudinal  slice  of  tourmaline,  the  spot  is  alternately 
dark  and  bright  as  we  turn  the  crystal  through  successive 
quadrants.     Here  we  have  a  contrast  of  properties  (dark 
and  bright)  corresponding  to  a  contrast  of  positions,  (the 
position  of  a  line  east  and  west  being  contrasted  with 
the  position  north  and  south,)  which,  as  we  have  said,  is 
the  general  character  of  polarity.     It  was  with  a  view  of 
expressing  this  character  that  the  term  polarization  was 
originally  introduced.     Malus  was  forced  by  his  disco- 
veries into  the  use  of  this  expression.     "  We  find,"  he 
says,  in  1811,  "  that  light  acquires  properties  which  are 
relative  only  to  the  sides  of  the  ray, — which  are  the  same 
for  the  north  and   south  sides  of  the  ray,  (using  the 
points  of  the  compass  for  description's  sake  only,)  and 
which  are  different  when  we  go  from  the  north  and  south 
to  the  east  or  to  the  west  sides  of  the  ray.     I  shall  give 
the  name  of  poles  to  these  sides  of  the  ray,  and  shall  call 
polarization  the  modification  which  gives  to  light  these 
properties  relative  to  these  poles.    I  have  put  off  hitherto 
the  admission  of  this  term  into  the  description  of  the 
physical  phenomena  with  which  we  have  to  do:   I  did 
not  date  to  introduce  it  into  the  Memoirs  in  which  I 
published  my  last  observations :  but  the  variety  of  forms 
in  which  this  new  phenomenon  appears,  and  the  difficulty 
of  describing  them,  compel  me  to  admit  this  new  expres- 
sion ;  which  signifies  simply  the  modification  which  light 
has  undergone  in  acquiring  new  properties  which  are  not 
relative  to  the  direction  of  the  ray,  but  only  to  its  sides 
considered  at  right  angles  to  each  other,  and  in  a  plane 
perpendicular  to  its  direction." 

The  theory  which  represents  light  as  an  emission  of 


APPLICATION  OF  THE  IDEA  OF  POLARITY.  337 

particles  was  in  vogue  at  the  time  when  Malus  published 
his  discoveries;  and  some  of  his  followers  in  optical 
research  conceived  that  the  phenomena  which  he  thus 
described  rendered  it  necessary  to  ascribe  poles  and  an 
axis  to  each  particle  of  light.  On  this  hypothesis,  light 
would  be  polarized  when  the  axes  of  all  the  particles 
were  in  the  same  direction :  and,  making  such  a  suppo- 
sition, it  may  easily  be  conceived  capable  of  transmission 
through  a  crystal  whose  axis  is  parallel  to  that  of  the 
luminous  particles,  and  intransmissible  when  the  axis  of 
the  crystal  is  in  a  position  transverse  to  that  of  the  par- 
ticles. 

The  hypothesis  of  particles  possessing  poles  is  a  rude 
and  arbitrary  assumption,  in  this  as  in  other  cases ;  but  it 
serves  to  convey  the  general  notion  of  polarity,  which  is 
the  essential  feature  of  the  phenomena.  The  term 
"  polarization  of  light"  has  sometimes  been  complained  of 
in  modern  times  as  hypothetical  and  obscure.  But  the 
real  cause  of  obscurity  was,  that  the  Idea  of  Polarity  was, 
till  lately,  very  imperfectly  developed  in  men's  minds. 
As  we  have  seen,  the  general  notion  of  polarity, — oppo- 
site properties  in  opposite  directions, — exactly  describes 
the  character  of  the  optical  phenomena  to  which  the 
term  is  applied. 

It  is  to  be  recollected  that  in  optics  we  never  speak 
of  the  poles,  but  of  the  plane  of  polarization  of  a  ray.  The 
word  sides,  which  Newton  and  Malus  have  used,  neither 
of  them  appears  to  have  been  satisfied  with ;  Newton,  in 
employing  it,  had  recourse  to  the  strange  Gallicism  of 
speaking  of  the  coast  of  usual  and  of  unusual  refraction 
of  a  crystal. 

The  modern  theory  of  optics  represents  the  plane  of 

polarization  of  light  as  depending,  not  on  the  position  in 

which  the  axes  of  the  luminiferous  particles  lie,  but  on 

the  direction  of  those  transverse  vibrations  in  which  light 

VOL.  i.  z 


338     PHILOSOPHY  OF  THE  MECHANICO-CHEMICAL  SCIENCES. 

consists.  This  theory  is,  as  we  have  stated  in  the  His- 
tory, recommended  by  an  extraordinary  series  of  suc- 
cesses in  accounting  for  the  phenomena.  And  this 
hypothesis  of  transverse  vibrations  shows  us  another 
mechanical  mode,  (besides  the  hypothesis  of  particles 
with  axes,)  by  which  we  may  represent  the  polarity  of  a 
ray.  But  we  may  remark  that  the  general  notion  of 
polarity,  as  applied  to  light  in  such  cases,  would  subsist, 
even  if  the  undulatory  theory  were  rejected.  The  idea 
is,  as  we  have  before  said,  independent  of  all  hypothetical 
machinery. 

I  need  not  here  refer  to  the  various  ways  in  which 
light  may  be  polarized,  as,  for  instance,  by  being  reflected 
from  the  surface  of  water  or  of  glass  at  certain  angles,  by 
being  transmitted  through  crystals,  and  in  other  ways. 
In  all  cases  the  modification  produced,  the  polarization, 
is  identically  the  same  property.  Nor  need  I  mention 
the  various  kinds  of  phenomena  which  appear  as  contrasts 
in  the  result ;  for  these  are  not  merely  light  and  dark,  or 
white  and  black,  but  red  and  green,  and  generally,  a 
colour  and  its  complementary  colour,  exhibited  in  many 
complex  and  varied  configurations.  These  multiplied 
modes  in  which  polarized  light  presents  itself  add  nothing 
to  the  original  conception  of  polarization:  and  I  shall 
therefore  pass  on  to  another  subject. 

6.  Crystallization. — Bodies  which  are  perfectly  crys- 
tallized exhibit  the  most  complete  regularity  and  sym- 
metry of  form ;  and  this  regularity  not  only  appears  in 
their  outward  shape,  but  pervades  their  whole  texture, 
and  manifests  itself  in  their  cleavage,  their  transparency, 
and  in  the  uniform  and  determinate  optical  properties 
which  exist  in  every  part,  even  the  smallest  fragment  of 
the  mass.  If  we  conceive  crystals  as  composed  of  par- 
ticles, we  must  suppose  these  particles  to  be  arranged  in 
the  most  regular  manner;  for  example,  if  we  suppose 


APPLICATION  OF  THE  IDEA  OF  POLARITY.  339 

each  particle  to  have  an  axis,  we  must  suppose  all  these 
axes  to  be  parallel ;  for  the  direction  of  the  axis  of  the 
particles  is  indicated  by  the  physical  and  optical  pro- 
perties of  the  crystal,  and  therefore  this  direction  must 
be  the  same   for   every  portion   of  the    crystal.     This 
parallelism  of  the  axes  of  the  particles   may  be   con- 
ceived to  result  from  the  circumstance  of  each  particle 
having  poles,  the  opposite  poles  attracting  each  other. 
In  virtue  of  forces  acting  as  this  hypothesis  assumes,  a 
collection   of    small   magnetic   particles   would   arrange 
themselves  in  parallel  positions ;  and  such  a  collection  of 
magnetic  particles  offers  a  sort  of  image  of  a  crystal. 
Thus  we  are  led  to  conceive  the  particles  of  crystals  as 
polarized,  and  as  determined  in  their  crystalline  positions 
by  polar  forces.     This  mode  of  apprehending  the  consti- 
tution of  crystals  has  been  adopted  by  some  of  our  most 
eminent   philosophers.      Thus   Berzelius    says*,    "  It   is 
demonstrated,  that  the  regular  forms  of  bodies  presuppose 
an  effort  of  their  atoms  to  touch  each  other  by  preference 
in  certain  points ;  that  is,  they  are  founded  upon  a  Pola- 
rity ;" — he  adds,  "  a  polarity  which  can  be  no  other  than 
an  electric  or  magnetic  polarity."     In  this  latter  clause 
we    have   the   identity   of    different   kinds   of    polarity 
asserted;    a  principle  which  we  shall  speak  of  in  the 
next  chapter.     But  we  may  remark,  that  even  without 
dwelling  upon  this  connexion,  any  notion  which  we  can 
form  of  the  structure  of  crystals  necessarily  involves  the 
idea   of    polarity.      Whether    this    polarity   necessarily 
requires  us  to  believe  crystals  to  be  composed  of  atoms 
which  exert  an  effort  to  touch  each  other  in  certain  points 
by  preference,  is  another  question.     And,  in  agreement 
with  what  has  been  said  respecting  other  kinds  of  polarity, 
we  shall  probably  find,  on  a  more  profound  examination 
of  the  subject,  that  while  the  idea  of  polarity  is  essential, 

*  Essay  on  the  Theory  of  Chemical  Properties,  1820,  p.  1 13. 

Z  2 


340    PHILOSOPHY  OF  THE  MECHANICO-CHEMICAL  SCIENCES. 

the  machinery  by  which  it  is  thus  expressed  is  precarious 
and  superfluous. 

7.  Chemical  Affinity. — We  shall  have,  in  the  next 
Book,  to  speak  of  Chemical  Affinity  at  some  length ;  but 
since  the  ultimate  views  to  which  philosophers  have  been 
led,  induce  them  to  consider  the  forces  of  affinity  as 
polar  forces,  we  must  enumerate  these  among  the  exam- 
ples of  polarity.  In  chemical  processes,  opposites  tend 
to  unite,  and  to  neutralize  each  other  by  their  union. 
Thus  an  acid  or  an  alkali  combine  with  vehemence,  and 
form  a  compound,  a  neutral  salt,  which  is  neither  acid 
nor  alkaline. 

This  conception  of  contrariety  and  mutual  neutraliza- 
tion, involves  the  idea  of  polarity.  In  the  conception,  as 
entertained  by  the  earlier  chemists,  the  idea  enters  very 
obscurely  :  but  in  the  attempts  which  have  more  recently 
been  made  to  connect  this  relation  (of  acid  and  base,)  with 
other  relations,  the  chemical  elements  have  been  conceived 
as  composed  of  particles  which  possess  poles ;  like  poles 
repelling,  and  unlike  attracting  each  other,  as  they  do  in 
magnetic  and  electric  phenomena.  This  is,  however,  a  rude 
and  arbitrary  way  of  expressing  polarity,  and,  as  may  be 
easily  shown,  involves  many  difficulties  which  do  not 
belong  to  the  idea  itself.  Mr.  Faraday,  who  has  been 
led  by  his  researches  to  a  conviction  of  the  polar  nature 
of  the  forces  of  chemical  affinity,  has  expressed  their 
character  in  a  more  general  manner,  and  without  any  of 
the  machinery  of  particles  indued  with  poles.  Accord- 
ing to  his  view,  chemical  synthesis  and  analysis  must 
always  be  conceived  as  taking  place  in  virtue  of  equal 
and  opposite  forces,  by  which  the  particles  are  united  or 
separated.  These  forces,  by  the  very  circumstance  of 
their  being  polar,  may  be  transferred  from  point  to  point. 
For  if  we  conceive  a  string  of  particles,  and  if  the  positive 
force  of  the  first  particle  be  liberated  and  brought  into 


APPLICATION  OF  THE  IDEA  OF  POLARITY.  341 

action,  its  negative  force  also  must  be  set  free :  this 
negative  force  neutralizes  the  positive  force  of  the  next 
particle,  and  therefore  the  negative  force  of  this  particle 
(before  employed  in  neutralizing  its  positive  force,)  is  set 
free  :  this  is  in  the  same  way  transferred  to  the  next 
particle,  and  so  on.  And  thus  we  have  a  positive  force 
active  at  one  extremity  of  a  line  of  particles,  correspond- 
ing to  a  negative  force  at  the  other  extremity,  all  the 
intermediate  particles  reciprocally  neutralizing  each  other's 
action.  This  conception  of  the  transfer  of  chemical  action 
was  indeed  at  an  earlier  period  introduced  by  Grotthus*, 
and  confirmed  by  Davy.  But  in  Mr.  Faraday's  hands 
we  see  it  divested  of  all  that  is  superfluous,  and  spoken 
of,  not  as  a  line  of  particles,  but  as  "  an  axis  of  power, 
having  [at  every  point,]  contrary  forces,  exactly  equal, 
in  opposite  directions." 

8.  General  Remarks. — Thus,  as  we  see,  the  notion  of 
polarity  is  applicable  to  many  large  classes  of  phenomena. 
Yet  the  idea  in  a  distinct  and  general  form  is  only  of 
late  growth  among  philosophers.  It  has  gradually  been 
abstracted  and  refined  from  many  extraneous  hypotheses 
which  were  at  first  supposed  to  be  essential  to  it.  We 
have  noticed  some  of  these  hypotheses ; — as  the  poles  of 
a  body ;  the  poles  of  the  particles  of  a  fluid ;  two  oppo- 
site fluids ;  a  single  fluid  in  excess  and  defect ;  transverse 
vibrations.  To  these  others  might  be  added.  Thus  Dr. 
Proutf  assumes  that  the  polarity  of  molecules  results 
from  their  rotation  on  their  axes,  the  opposite  motions 
of  contiguous  molecules  being  the  cause  of  opposite 
(positive  and  negative)  polarities. 

But  none  of  these  hypotheses  can  be  proved  by  the 
fact  of  polarity  alone ;  and  they  have  been  in  succession 
rejected  when  they  had  been  assumed  on  that  ground. 

*  DUMAS,  Lemons  sur  la  Philosophic  Chimique,  p.  401 . 
t  Bridgwater  Treatise,  p.  559. 


342     PHILOSOPHY  OF  THE  MECHANICO-CHEMICAL  SCIENCES. 

Thus  Davy,  in  1826,  speaking  of  chemical  forces  says*, 
"  In  assuming  the  idea  of  two  ethereal,  subtile,  elastic 
fluids,  attractive  of  the  particles  of  each  other,  and 
repulsive  as  to  their  own  particles,  capable  of  combining 
in  different  proportions  with  bodies,  and  according  to 
their  proportions  giving  them  their  specific  qualities  and 
rendering  them  equivalent  masses,  it  would  be  natural 
to  refer  the  action  of  the  poles  to  the  repulsions  of  the 
substances  combined  with  the  excess  of  one  fluid,  and 
the  attractions  of  those  united  to  the  excess  of  the  other 
fluid  ;  and  a  history  of  the  phenomena,  not  unsatisfactory 
to  the  reason,  might  in  this  way  be  made  out.  But  as  it 
is  possible  likewise  to  take  an  entirely  different  view  of 
the  subject,  on  the  idea  of  the  dependence  of  the  results 
upon  the  primary  attractive  powers  of  the  parts  of  the 
combination  on  a  single  subtile  fluid,  I  shall  not  enter 
into  any  discussion  on  this  obscure  part  of  the  theory." 
Which  of  these  theories  will  best  represent  the  case,  will 
depend  upon  the  consideration  of  other  facts,  in  combi- 
nation with  the  polar  phenomena,  as  we  see  in  the  history 
of  optical  theory.  In  like  manner  Mr.  Faraday  proved 
by  experiment  f  the  error  of  all  theories  which  ascribe 
electro-chemical  decomposition  to  the  attraction  of  the 
poles  of  the  voltaic  battery. 

In  order  that  they  may  distinctly  image  to  them- 
selves the  idea  of  polarity,  men  clothe  it  in  some  of 
the  forms  of  machinery  above  spoken  of;  yet  every 
new  attempt  shows  them  the  unnecessary  difficulties  in 
which  they  thus  involve  themselves.  But  on  the  other 
hand  it  is  difficult  to  apprehend  this  idea  divested  of 
all  machinery;  and  to  entertain  it  in  such  a  form  that 
it  shall  apply  at  the  same  time  to  magnetism  and  elec- 
tricity, galvanism  and  chemistry,  crystalline  structure  and 
light.  The  Idea  of  Polarity  becomes  most  pure  and  genu- 

*  Phil.  Tr.9  1826,  p.  415.  t  Researches,  p.  495,  &c. 


APPLICATION  OF  THE  IDEA  OF  POLARITY.  343 

ine,  when  we  entirely  reject  the  conception  of  Poles,  as 
Faraday  has  taught  us  to  do  in  considering  electro-chemical 
decomposition ;  but  it  is  only  by  degrees  and  by  effort  that 
we  can  reach  this  point  of  abstraction  and  generality. 

9.  There  is  one  other  remark  which  we  may  here  make. 
It  was  a  maxim  commonly  received  in  the  ancient  schools 
of  philosophy,  that  "  like  attracts  like:"  but  as  we  have 
seen,  the  universal  maxim  of  polar  phenomena  is,  that 
like  repels  like,  and  attracts  unlike.  The  north  pole 
attracts  the  south  pole,  the  positive  fluid  attracts  the 
negative  fluid ;  opposite  elements  rush  together ;  opposite 
motions  reduce  each  other  to  rest.  The  permanent  and 
stable  course  of  things  is  that  which  results  from  the 
balance  and  neutralization  of  contrary  tendencies. 
Nature  is  constantly  labouring  after  repose  by  the  effect 
of  such  tendencies ;  and  so  far  as  polar  forces  enter  into 
her  economy,  she  seeks  harmony  by  means  of  discord, 
and  unity  by  opposition. 

Although  the  Idea  of  Polarity  is  still  somewhat  vague 
and  obscure,  even  in  the  minds  of  the  cultivators  of 
physical  science,  it  has  still  given  birth  to  some  general 
principles  which  have  been  accepted  as  evident,  and 
have  had  great  influence  on  the  progress  of  science. 
These  we  shall  now  consider. 


CHAPTER  II. 
OF  THE  CONNEXION  OF  POLARITIES. 

1.  IT  has  appeared  in  the  preceding  chapter  that  in 
cases  in  which  the  phenomena  suggest  to  us  the  idea  of 
polarity,  we  are  also  led  to  assume  some  material  ma- 
chinery as  the  mode  in  which  the  polar  forces  are  exerted. 
We  assume,  for  instance,  globular  particles  which  possess 


344     PHILOSOPHY  OF  THE  MECHANICO-CHEMICAL  SCIENCES. 

poles,  or  the  vibrations  of  a  fluid,  or  two  fluids  attracting 
each  other;  in  every  case,  in  short,  some  hypothesis  by 
which  the  existence  and  operation  of  the  polarity  is 
embodied  in  geometrical  and  mechanical  properties  of  a 
medium;  nor  is  it  possible  for  us  to  avoid  proceeding 
upon  the  conviction  that  some  such  hypothesis  must  be 
true ;  although  the  nature  of  the  connexion  between 
the  mechanism  and  the  phenomena  must  still  be  inde- 
finite and  arbitrary. 

But  since  each  class  of  polar  phenomena  is  thus 
referred  to  an  ulterior  cause,  of  which  we  know  no  more 
than  that  it  has  a  polar  character,  it  follows  that  different 
polarities  may  result  from  the  same  cause  manifesting 
its  polar  character  under  different  aspects.  Taking,  for 
example,  the  hypothesis  of  globular  particles,  if  electricity 
result  from  an  action  dependent  upon  the  poles  of  each 
globule,  magnetism  may  depend  upon  an  action  in  the 
equator  of  each  globule;  or  taking  the  supposition  of 
transverse  vibrations,  if  polarized  light  result  directly 
from  such  vibrations,  crystallization  may  have  reference 
to  the  axes  of  the  elasticity  of  the  medium  by  which  the 
vibrations  are  rendered  transverse, — so  far  as  the  polar 
character  only  of  the  phenomena  is  to  be  accounted  for.  I 
say  this  may  be  so,  in  so  far  only  as  the  polar  character  of 
the  phenomena  is  concerned ;  for  whether  the  relation  of 
electricity  to  magnetism,  or  of  crystalline  forces  to  light, 
can  really  be  explained  by  such  hypotheses,  remains  to 
be  determined  by  the  facts  themselves.  But  since  the 
first  necessary  feature  of  the  hypothesis  is,  that  it  shall 
give  polarity,  and  since  an  hypothesis  which  does  this  may, 
by  its  mathematical  relations,  give  polarities  of  different 
kinds  and  in  different  directions,  any  two  co-existent 
kinds  of  polarity  may  result  from  the  same  cause,  mani- 
festing itself  in  various  manners. 

The  conclusion  to  which  we  are  led  by  these  general 


OF  THE  CONNEXION  OF  POLARITIES.  345 

considerations  is,  that  two  co-existing  classes  of  polar 
phenomena  may  be  effects  of  the  same  cause.  But  those 
who  have  studied  such  phenomena  more  deeply  and 
attentively  have,  in  most  or  in  all  cases,  arrived  at  the 
conviction  that  the  various  kinds  of  polarity  in  such  cases 
must  be  connected  and  fundamentally  identical.  As  this 
conviction  has  exercised  a  great  influence,  both  upon  the 
discoveries  of  new  facts  and  upon  the  theoretical  specu- 
lations of  modern  philosophers,  and  has  been  put  forward 
by  some  writers  as  a  universal  principle  of  science,  I  will 
consider  some  of  the  cases  in  which  it  has  been  thus 
applied. 

2.  Connexion  of  *  Magnetic  and  Electric  Polarity. — 
The  polar  phenomena  of  electricity  and  magnetism  are 
clearly  analogous  in  their  laws  :  and  obvious  facts  showed 
at  an  early  period  that  there  was  some  connexion  between 
the  two  agencies.  Attempts  were  made  to  establish  an 
evident  and  definite  relation  between  the  two  kinds  of 
force,  which  attempts  proceeded  upon  the  principle  now 
under  consideration ; — namely,  that  in  such  cases,  the  two 
kinds  of  polarity  must  be  connected.  Professor  (Ersted, 
of  Copenhagen,  was  one  of  those  who  made  many  trials 
founded  upon  this  conviction :  yet  all  these  were  long 
unsuccessful.  At  length,  in  1820,  he  discovered  that  a 
galvanic  current,  passing  at  right  angles  near  to  a  mag- 
netic needle,  exercises  upon  it  a  powerful  deflecting 
force.  The  connexion  once  detected  between  magnetism 
and  galvanism  was  soon  recognised  as  constant  and 
universal.  It  was  represented  in  different  hypothetical 
modes  by  different  persons;  some  considering  the  gal- 
vanic current  as  the  primitive  axis,  and  the  magnet  as 
constituted  of  galvanic  currents  passing  round  it  at  right 
angles  to  the  magnetic  axis;  while  others  conceived  the 
magnetic  axis  as  the  primitive  one,  and  the  electric 
current  as  implying  a  magnetic  current  round  the  wire. 


346     PHILOSOPHY  OF  THE  MECHANICO-CHEMICAL  SCIENCES. 

So  far  as  many  of  the  general  relations  of  these  two  kinds 
of  force  were  concerned,  either  mode  of  representation 
served  to  express  them ;  and  thus  the  assumption  that 
the  two  polarities,  the  magnetic  and  the  electric,  were 
fundamentally  identical,  was  verified,  so  far  as  the  phe- 
nomena of  magnetic  attraction,  and  the  like,  were  con- 
cerned. 

I  need  not  here  mention  how  this  was  further  con- 
firmed by  the  experiments  in  which,  by  means  of  the 
forces  thus  brought  into  view,  a  galvanic  wire  was  made 
to  revolve  round  a  magnet,  and  a  magnet  round  a  gal- 
vanic wire ;  in  which  artificial  magnets  were  constructed 
of  coils  of  galvanic  wire ;  and  finally,  in  which  the  gal- 
vanic spark  was  obtained  from  the  magnet.  The  identity 
which  sagacious  speculators  had  divined  even  before  it 
was  discovered,  and  which  they  had  seen  to  be  universal  as 
soon  as  it  was  brought  to  light,  was  completely  manifested 
in  every  imaginable  form. 

The  relation  of  the  electric  and  magnetic  polarities 
was  found  to  be,  that  they  were  transverse  to  each  other, 
and  this  relation  exhibited  under  various  conditions  of 
form  and  position  of  the  apparatus,  gave  rise  to  very 
curious  and  unexpected  perplexities.  The  degree  of  com- 
plication which  this  relation  may  occasion,  may  be  judged 
of  from  the  number  of  constructions  and  modes  of  con- 
ception offered  by  (Ersted,  Wollaston,  Faraday,  and  others, 
for  the  purpose  of  framing  a  technical  memory  of  the 
results.  The  magnetic  polarity  gives  us  the  north  and 
south  poles  of  the  needle ;  the  electric  polarity  makes  the 
current  positive  and  negative ;  and  these  pairs  of  opposites 
are  connected  by  relations  of  situation,  as  above  and  below, 
right  and  left ;  and  give  rise  to  the  resulting  motion  of 
the  needle  one  way  or  the  other. 

3.  Ampere,  by  framing  his  hypotheses  of  the  action  of 
voltaic  currents  and  the  constitution  of  magnets,  reduced 


OF  THE  CONNEXION  OF  POLARITIES.  347 

all  these  technical  rules  to  rigorous  deductions  from  one 
general  principle.  And  thus  the  vague  and  obscure  per- 
suasion that  there  must  be  some  connexion  between  elec- 
tricity and  magnetism,  so  long  an  idle  and  barren  conjec- 
ture, was  unfolded  into  a  complete  theory,  according  to 
which  magnetic  and  electromotive  actions  are  only  two 
different  manifestations  of  the  same  forces ;  and  all  the 
above-mentioned  complex  relations  of  polarities  are  re- 
duced to  one  single  polarity,  that  of  the  electro-dynamic 
current. 

4.  As  the  idea  of  polarity  was  thus  firmly  established 
and  clearly  developed,  it  became  an  instrument  of  reason- 
ing. Thus  it  led  Ampere  to  maintain  that  the  original 
or  elementary  forces  in  electro-dynamic  action  could  not 
be  as  M.  Biot  thought  they  were,  a  statical  couple,  but 
must  be  directly  opposite  to  each  other.  The  same  idea 
enabled  Mr.  Faraday  to  carry  on  with  confidence  such 
reasonings  as  the  following  #  :  "  No  other  known  power 
has  like  direction  with  that  exerted  between  an  electric 
current  and  a  magnetic  pole ;  it  is  tangential,  while  all 
other  forces  acting  at  a  distance  are  direct.  Hence  if  a 
magnetic  pole  on  one  side  of  a  revolving  plate  follow  its 
course  by  reason  of  its  obedience  to  the  tangential  force 
exerted  upon  it  by  the  very  current  of  electricity  which 
it  has  itself  caused ;  a  similar  pole  on  the  other  side  of 
the  plate  should  immediately  set  it  free  from  this  force ; 
for  the  currents  which  have  to  be  formed  by  the  two 
poles  are  in  contrary  directions."  And  in  Article  1114 
of  his  Researches,  the  same  eminent  philosopher  infers 
that  if  electricity  and  magnetism  are  considered  as  the 
results  of  a  peculiar  agent  or  condition,  exerted  in  deter- 
minate directions  perpendicular  to  each  other,  one  must 
be  by  some  means  convertible  into  the  other ;  and  this 
he  was  afterwards  able  to  prove  to  be  the  case  in  fact. 

*  Researches,  244. 


348     PHILOSOPHY  OF  THE  MECHANICO-CHEMICAL  SCIENCES. 

Thus  the  principle  that  .the  co-existent  polarities  of 
magnetism  and  electricity  are  connected  and  fundamen- 
tally identical,  is  not  only  true,  but  is  far  from  being 
either  vague  or  barren.  It  has  been  a  fertile  source  both 
of  theories  which  have,  at  present,  a  very  great  probabi- 
lity, and  of  the  discovery  of  new  and  striking  facts.  We 
proceed  to  consider  other  similar  cases. 

5.  Connexion  of  Electrical  and  Chemical  Polarities. — 
The  doctrine  that  the  chemical  forces  by  which  the  ele- 
ments of  bodies  are  held  together  or  separated,  are  iden- 
tical with  the  polar  forces  of  electricity,  is  a  great  dis- 
covery of  modern  times ;  so  great  and  so  recent,  indeed, 
that  probably  men  of  science  in  general  have  hardly  yet 
obtained  a  clear  view  and  firm  hold  of  this  truth.  This 
doctrine  is  now,  however,  entirely  established  in  the  minds 
of  the  most  profound  and  philosophical  chemists  of  our 
time.  The  complete  developement  and  confirmation  of 
this  as  of  other  great  truths,  was  preceded  by  more  vague 
and  confused  opinions  gradually  tending  to  this  point; 
and  the  progress  of  thought  and  of  research  was  impelled 
and  guided,  in  this  as  in  similar  cases,  by  the  persuasion 
that  these  co-existent  polarities  could  not  fail  to  be  closely 
connected  with  each  other.  While  the  ultimate  and 
exact  theory  to  which  previous  incomplete  and  transitory 
theories  tended  is  still  so  new  and  so  unfamiliar,  it  must 
needs  be  a  matter  of  difficulty  and  responsibility  for  a 
common  reader  to  describe  the  steps  by  which  truth  has 
advanced  from  point  to  point.  I  shall,  therefore,  in  doing 
this,  guide  myself  mainly  by  the  historical  sketches  of 
the  progress  of  this  great  theory,  which,  fortunately  for  us, 
have  been  given  us  by  the  two  philosophers  who  have 
played  by  far  the  most  important  parts  in  the  discovery, 
Davy  and  Faraday. 

It  will  be  observed  that  we  are  concerned  here  with 
the  progress  of  theory,  and  not  of  experiment,  except  so 


OF  THE  CONNEXION  OF  POLARITIES.  349 

far  as  it  is  confirmatory  of  theory.     In  Davy's  Memoir* 
of  1826,  on  the  Relations  of  Electrical  and  Chemical 
Changes,  he  gives  the  historical  details  to  which  I  have 
alluded.     Already  in  1802  he  had  conjectured  that  all 
chemical  decompositions  might  be   polar.     In   1806  he 
attempted  to  confirm  this  conjecture,  and  succeeded,  to 
his  own  satisfaction,  in  establishing!  that  the  combina- 
tions  and   decompositions  by  electricity  were  referable 
to  the  law  of  electrical  attractions  and  repulsions ;  and 
advanced  the  hypothesis  (as  he  calls  it,)  that  chemical  and 
electrical  attractions  were  produced  by  the  same  cause, 
acting  in  one  case  on  particles,  in  the  other  on  masses. 
This  hypothesis  was  most  strikingly  confirmed   by  the 
author's  being  able  to  use  electrical  agency  as  a  more 
powerful  means  of    chemical    decomposition  than    any 
which  had  yet  been  applied.     "  Believing,"  he  adds,  "  that 
our  philosophical  systems  are  exceedingly  imperfect,  I 
never  attached  much  importance  to  this  hypothesis ;  but 
having  formed  it  after  a  copious  induction  of  facts,  and 
having  gained  by  the  application  of  it  a  number  of  prac- 
tical results,  and  considering  myself  as  much  the  author 
of  it  as  I  was  of  the  decomposition  of  the  alkalies,  and 
having  developed  it  in  an  elementary  work  as  far  as  the 
present  state  of  chemistry  seemed  to  allow,  I  have  never," 
he  says,  "  criticized  or  examined  the  manner  in  which 
different  authors  have  adopted  or  explained  it,  contented, 
if  in  the  hands  of  others,  it  assisted  the  arrangements  of 
chemistry  or  mineralogy,  or  became  an  instrument  of  dis- 
covery."    When  the  doctrine  had  found   an  extensive 
acceptance  among  chemists,  attempts  were  made  tB  show 
that  it  had  been  asserted  by  earlier  writers :  and  though 
Davy  justly  denies  all  value  to  these  pretended  anticipa- 
tions, they  serve  to  show,  however  dimly,  the  working  of 
that  conviction  of  the  connexion  of  co-existent  proper- 
*  Phil.  Trans.,  1826,  p.  383.  t  P.  389. 


350     PHILOSOPHY  OF  THE  MECHANICO-CHEMICAL  SCIENCES. 

ties  which  all  along  presided  in  men's  minds  during  this 
course  of  investigation.     "  Bitter  and  Winterl  have  been 
quoted,"  Davy  says*1,  "among  other   persons,    as  having 
imagined  or  anticipated  the  relation   between  electrical 
powers  and  chemical  affinities  before  the  discovery  of  the 
pile  of  Volta.     But  whoever  will   read   with  attention 
Hitter's   '  Evidence   that  Galvanic  action  exists  in  orga- 
nized   nature,'   and    Winter's   Prolusiones  ad   Chemiam 
scBculi  decimi  noni,  will  find  nothing  to  justify  this  opi- 
nion."    He  then  refers  to  the  Queries  of  Newton  at  the 
end  of  his  Optics.     "These,"   he   says,    "contain   more 
grand  and  speculative  views  that  might  be  brought  to 
bear  upon  this  question  than  any  found  in  the  works  of 
modern  electricians ;  but  it  is  very  unjust  to  the  experi- 
mentalists who  by  the  laborious  application  of  new  in- 
struments, have  discovered  novel  facts  and  analogies,  to 
refer  them  to  any  such  suppositions  as  that  all  attractions, 
chemical,  electrical,  magnetical,  and  gravitative,  may  de- 
pend upon  the  same  cause."     It  is  perfectly  true,  that 
such  vague  opinions,  though  arising  from  that  tendency  to 
generalize  which  is  the  essence  of  science,  are  of  no  value 
except  so  far  as  they  are  both  rendered  intelligible,  and 
confirmed  by  experimental  research. 

The  phenomena  of  chemical  decomposition  by  means 
of  the  voltaic  pile,  however,  led  other  persons  to  views 
very  similar  to  those  of  Davy.  Thus  Grotthus  in  1805f 
published  an  hypothesis  of  the  same  kind.  "The  pile  of 
Volta,"  he  says,  "  is  an  electrical  magnet,  of  which  each 
element,  that  is,  each  pair  of  plates,  has  a  positive  and  a 
negative  pole.  The  consideration  of  this  polarity  sug- 
gested to  me  the  idea  that  a  similar  polarity  may  come 
into  play  between  the  elementary  particles  of  water 
when  acted  upon  by  the  same  electrical  agent ;  and  I 
avow  that  this  thought  was  for  me  a  flash  of  light." 

*  Phil.  Trans.,  1826,  p.  384.  f  ***•  Chim.;  Ixriii.,  54. 


OF  THE  CONNEXION  OF  POLARITIES.  351 

6.  The  thought,  however,  though  thus  brought  into 
being,  was  very  far  from  being  as  yet  freed  from  vague- 
ness, superfluities,  and  errors.     I  have  elsewhere  noticed* 
Faraday's  remark  on  Davy's  celebrated  Memoir  of  1806 ; 
that  "  the  mode  of  action  by  which  the  effects  take  place 
is  stated  very  generally,  so  generally,  indeed,  that  probably 
a  dozen  precise  schemes  of  electro-chemical  action  might 
be  drawn  up,  differing  essentially  from  each  other,  yet  all 
agreeing  with  the  statement  there  given."     When  Davy 
and  others  proceeded  to  give  a  little  more  definiteness 
and  precision  to  the  statement  of  their  views,  they  soon 
introduced  into  the  theory  features  which  it  was  after- 
wards found  necessary  to  abandon.     Thusf  both  Davy, 
Grotthus,  Riffault,  and  Chompre,  ascribed  electrical  de- 
composition to  the  action  of  the  poles,  and  some  of  them 
even  pretended  to  assign  the  proportion  in  which  the 
force  of  the  pole  diminishes  as  the  distance  from  it  in- 
creases.    Faraday,  as  I  have  already  stated,  showed  that 
the  polarity  must  be  considered  as  residing  not  only  in 
what  had  till  then  been  called  the  poles,  but  at   every 
point  of  the  circuit.    He  ascribed^:   electro-chemical  de- 
composition to  internal  forces,  residing  in  the  particles  of 
the  matter  under  decomposition,  not  to   external  forces, 
exerted  by  the  poles.     Hence  he  shortly  afterwards  §  pro- 
posed to  reject  the  word  poles  altogether,  and  to  employ 
instead,  the  term  electrode,  meaning  the  doors  or  passages 
(of  whatever  surface  formed,)  by  which  the  decomposed 
elements  pass  out.     What  have  been  called  the  positive 
and    negative  poles  he   further   termed    the  anode  and 
cathode ;  and  he  introduced   some  other  changes  in  no- 
menclature connected  with  these.      He  then,  as  I  have 

*  Hist.  Ind.  Sci.,  iii.  161. 

t  See  FARADAY'S  Historical  Sketch,  Researches,  481 — 492. 

f  Art.  524. 

§  Iri  1834.     Eleventh  Series  of  Researches.    Art.  662. 


352     PHILOSOPHY  OF  THE  MECHANICO-CHEMICAL  SCIENCES. 

related  in  the  History*,  invented  the  Volta-electrometer, 
which  enabled  him  to  measure  the  quantity  of  voltaic 
action,  and  this  he  found  to  be  identical  \vith  the  quantity 
of  chemical  affinity ;  and  he  was  thus  led  to  the  clearest 
view  of  the  truth  towards  which  he  and  his  predecessors 
had  so  long  been  travelling,  that  electrical  and  chemical 
forces  are  identical  f. 

7.  It  will,  perhaps,  be  said  that  this  beautiful  train  of 
discovery  was  entirely  due  to  experiment,  and  not  to  any 
a  priori  conviction  that  co-existent  polarities  must  be 
connected.     I  trust  I  have  sufficiently  stated  that  such 
an  a  priori  principle  could  not  be  proved,  nor  even  under- 
stood, without  a  most  laborious  and  enlightened  use  of 
experiment ;  but  yet  I  think  that  the  doctrine  when  once 
fully  unfolded,  exhibited  clearly,  and  established  as  true, 
takes  possession  of  the  mind  with  a  more  entire  convic- 
tion of  its    certainty  and  universality,  in  virtue  of  the 
principle  we  are  now  considering.     When  the  theory  has 
assumed  so  simple  a  form,  it  appears  to  derive  immense 
probability  (to  say  the  least)  from  its  simplicity.     Like 
the  laws  of  motion,  when  stated  in  its  most  general  form, 
it  appears  to  carry  with  it  its  own  evidence.     And  thus 
this  great  theory  borrows  something  of  its  character  from 
the  Ideas  which  it  involves,  as  well  as  from  the  experi- 
ments by  which  it  was  established. 

8.  We  may  find  in  many  of  Mr.  Faraday's  subsequent 
reasonings,  clear  evidence  that  this  idea  of  the  connexion 
of  polarities,  as  now  developed,  is  not  limited  in  its  appli- 
cation to  facts  already  known  experimentally,  but,  like 
other  ideas,  determines  the  philosopher's  researches  into 
the  unknown,  and  gives  us  the  form  of  knowledge  even 
before  we  possess  the  matter.    Thus,  he  says,  in  his  Thir- 
teenth Series t,  "I  have  long  sought,  and  still  seek,  for  an 
effect  or  condition  which  shall  be  to  statical  electricity 

*  Hist.  Ind.  Sci.,  iii.,  168.       t  Art.  915,  916,  917.     }  Art,  1658. 


OF  THE  CONNEXION  OF  POLARITIES.  353 

what  magnetic  force  is  to  current  electricity ;  for  as  the 
lines  of  discharge  are  associated  with  a  certain  transverse 
effect,  so  it  appeared  to  me  impossible  but  that  the  lines 
of  tension  or  of  inductive  action,  which  of  necessity  pre- 
cede the  discharge,  should  also  have  their  correspondent 
transverse  condition  or  effect."  Other  similar  passages 
might  be  found. 

I  will  now  consider  another  case  to  which  we  may 
apply  the  principle  of  connected  polarities. 

9.  Connexion  of  Chemical  and  Crystalline  Polarities. 
-The  close  connexion  between  the  chemical  affinity 
and  the  crystalline  attraction  of  elements  cannot  be  over- 
looked. Bodies  never  crystallize  but  when  their  ele- 
ments combine  chemically ;  and  solid  bodies  which  com- 
bine, when  they  do  it  most  completely  and  exactly,  also 
crystallize.  The  forces  which  hold  together  the  elements 
of  a  crystal  of  alum  are  the  same  forces  which  make  it  a 
crystal.  There  is  no  distinguishing  between  the  two  sets 
of  forces. 

Both  chemical  and  crystalline  forces  are  polar,  as  we 
stated  in  the  last  chapter ;  but  the  polarity  in  the  two 
cases  is  of  a  different  kind.  The  polarity  of  chemical 
forces  is  then  put  in  the  most  distinct  form,  when  it  is 
identified  with  electrical  polarity;  the  polarity  of  the 
particles  of  crystals  has  reference  to  their  geometrical 
form.  And  it  is  clear  that  these  two  kinds  of  polarity 
must  be  connected.  Accordingly,  Berzelius  expressly 
asserts*  the  necessary  identity  of  these  two  polarities. 
"  The  regular  forms  of  bodies  suppose  a  polarity  which 
can  be  no  other  than  an  electric  or  magnetic  polarity." 
This  being  so  seemingly  inevitable,  we  might  expect  to 
find  the  electric  forces  manifesting  some  relation  to  the 
definite  directions  of  crystalline  forms.  Mr.  Faraday  tried, 
but  in  vain,  to  detect  some  such  relation.  He  attempted 

""  Essay  on  Chemical  Prop.,  1 13. 
VOL,  I.  2   A 


354     PHILOSOPHY  OF  THE  MECHANICO-CHEMICAL  SCIENCES. 

to  ascertain*  whether  a  cube  of  rock  crystal  transmitted 
the  electrical  force  of  tension  with  different  intensity 
along  and  across  the  axis  of  the  crystal.  In  the  first  spe- 
cimen there  seemed  to  be  some  difference ;  but  in  other 
experiments,  made  both  with  rock  crystal  and  with  calc 
spar,  this  difference  disappeared.  Although  therefore  we 
may  venture  to  assert  that  there  must  be  some  very  close 
connexion  between  electrical  and  crystalline  forces,  we 
are,  as  yet,  quite  ignorant  what  the  nature  of  the  con- 
nexion is,  and  in  what  kind  of  phenomena  it  will  manifest 
itself. 

10.  Connexion  of  Crystalline  and  Optical  Polarities. — 
Crystals  present  to  us  optical  phenomena  which  have  a 
manifestly  polar  character.     The  double  refraction,  both 
of  uniaxal  and  of  biaxal  crystals,  is  always  accompanied 
with  opposite  polarization  of  the  two  rays ;  and  in  this 
and  in  other  ways  light  is  polarized  in  directions  depen- 
dent upon   the  axes  of  the  crystalline  form,  that  is,  on 
the  directions  of  the  polarities  of  the  crystalline  particles. 
The  identity  of  these  two  kinds  of  polarity  (crystalline 
and  optical)  is  too  obviou  to  need  insisting  on  ;    and  it  is 
not  necessary  for  us  here  to  decide  by  what  hypothesis 
this  identity  may  most  properly  be  represented.     We 
may  hereafter  perhaps  find  ourselves  justified  in  consider- 
ing the  crystalline  forces  as  determining  the  elasticity  of 
the  luminiferous  ether  to  be  different  in  different  direc- 
tions within  the  crystal,  and  thus  as  determining  the 
refraction  and  polarization  of  the  light  which  the  crystal 
transmits.     But  at  present  we  merely  note  this  case  as 
an  additional  example  of  the  manifest  connexion   and 
fundamental  identity  of  two  co-existent  polarities. 

11.  Connexion  of  Polarities  in  general. — Thus  we  find 
that  the  connexion  of  different  kinds  of  polarities,  mag- 
netic, electric,  chemical,  crystalline,  and  optical,  is  certain 

*  Researches.    Art.  1689. 


OF  THE  CONNEXION  OF  POLARITIES.  355 

as  a  truth  of  experimental  science.  We  have  attempted 
to  show  further  that  in  the  minds  of  several  of  the  most 
eminent  discoverers  and  philosophers,  such  a  conviction 
is  something  more  than  a  mere  empirical  result :  it  is  a 
principle  which  has  regulated  their  researches  while  it 
was  still  but  obscurely  seen  and  imperfectly  unfolded,  and 
has  given  to  their  theories  a  character  of  generality  and 
self-evidence  which  experience  alone  cannot  bestow. 

It  will,  perhaps,  be  said  that  these  doctrines, — that 
scientific  researches  may  usefully  be  directed  by  prin- 
ciples in  themselves  vague  and  obscure ; — that  theories 
may  have  an  evidence  superior  to  and  anterior  to  experi- 
ence ; — are  doctrines  in  the  highest  degree  dangerous,  and 
utterly  at  variance  with  the  soundest  maxims  of  modern 
times  respecting  the  cultivation  of  science. 

To  the  justice  and  wisdom  of  this  caution  I  entirely 
agree  :  and  although  I  have  shown  that  this  principle  of 
the  connexion  of  polarities,  rightly  interpreted  and  esta- 
blished in  each  case  by  experiment,  involves  profound 
and  comprehensive  truths ;  I  think  it  no  less  important 
to  remark  that,  at  least  in  the  present  stage  of  our  know- 
ledge, we  can  make  no  use  of  this  principle  without 
taking  care,  at  every  step,  to  determine  by  clear  and  deci- 
sive experiments,  its  proper  meaning  and  application. 
All  endeavours  to  proceed  otherwise  have  led,  and  must 
lead,  to  ignorance  and  confusion.  Attempts  to  deduce 
from  our  bare  idea  of  polarity,  and  our  fundamental  con- 
victions respecting  the  connexion  of  polarities,  theories 
concerning  the  forces  which  really  exist  in  nature,  can 
hardly  have  any  other  result  than  to  bewilder  men's 
minds,  and  to  misdirect  their  efforts. 

So  far,  indeed,  as  this  persuasion  of  a  connexion 
among  apparently  different  kinds  of  agencies  impels  men, 
engaged  in  the  pursuit  of  knowledge,  to  collect  observa- 
tions, to  multiply,  repeat,  and  vary  experiments,  and  to 

2  A  2 


356     PHILOSOPHY  OF  THE  MECHANICO-CHEMTCAL  SCIENCES. 

contemplate  the  result  of  these  in  all  aspects  and  rela- 
tions, it  may  be  an  occasion  of  the  most  important  dis- 
coveries. Accordingly  we  find  that  the  great  laws  of 
phenomena  which  govern  the  motions  of  the  planets 
about  the  sun,  were  first  discovered  by  Kepler,  in  con- 
sequence of  his  scrutinizing  the  recorded  observations 
with  an  intense  conviction  of  the  existence  of  geome- 
trical and  arithmetical  harmonies  in  the  solar  system. 
Perhaps  we  may  consider  the  discovery  of  the  connexion 
of  magnetism  and  electricity  by  Professor  (Ersted  in  1820, 
as  an  example  somewhat  of  the  same  kind ;  for  he  also 
was  a  believer  in  certain  comprehensive  but  undefined 
relations  among  the  properties  of  bodies;  and  in  conse- 
quence of  such  views  entertained  great  admiration  for 
the  Prologue  to  the  Chemistry  of  the  Nineteenth  Century,  of 
Winterl,  already  mentioned.  M.  (Ersted,  in  1803,  pub- 
lished a  summary  of  this  work ;  and  in  so  doing,  praised 
the  views  of  Winterl  as  far  more  profound  and  compre- 
hensive than  those  of  Lavoisier.  Soon  afterwards  a 
Review  of  this  publication  appeared  in  France*,  in  which 
it  was  spoken  of  as  a  work  only  fit  for  the  dark  ages,  and 
as  the  indication  of  a  sect  which  had  for  some  time 
"ravaged  Germany,"  and  inundated  that  country  with 
extravagant  and  unintelligible  mysticism.  It  was,  there- 
fore, a  kind  of  triumph  to  M.  (Ersted  to  be,  after  some 
years'  labour,  the  author  of  one  of  the  most  remarkable 
and  fertile  physical  discoveries  of  his  time. 

12.  It  was  not  indeed  without  some  reason  that  cer- 
tain of  the  German  philosophers  were  accused  of  dealing  in 
doctrines  vast  and  profound  in  their  aspect,  but,  in  reality, 
indefinite,  ambiguous,  and  inapplicable.  And  the  most 
prominent  of  such  doctrines  had  reference  to  the  prin- 
ciple now  under  our  consideration  ;  they  represented  the 
properties  of  bodies  as  consisting  in  certain  polarities, 

*  Ann.  Ckim.,  torn.  50  (1804),  p.  191. 


Or  THE  CONNEXION  OF  POLARITIES.  357 

and  professed  to  deduce,  from  the  very  nature  of  things, 
with  little  or  no  reference  to  experiment,  the  existence 
and  connexion  of  these  polarities.  Thus  Schelling,  in 
his  Ideas  towards  a  Philosophy  of  Nature,  published  in 
1803,  says*,  "Magnetism  is  the  universal  act  of  investing 
Multiplicity  with  Unity ;  but  the  universal  form  of  the 
reduction  of  Multiplicity  to  Unity  is  the  Line,  pure  Lon- 
gitudinal Extension :  hence  Magnetism  is  determination 
of  pure  Longitudinal  Extension;  and  as  this  manifests 
itself  by  absolute  Cohesion,  Magnetism  is  the  determina- 
tion of  absolute  Cohesion."  And  as  Magnetism  was,  by 
such  reasoning,  conceived  to  be  proved  as  a  universal 
property  of  matter,  Schelling  asserted  ;t  to  be  a  confir- 
mation of  his  views  when  it  was  discovered  that  other 
bodies  besides  iron  are  magnetic.  In  like  manner  he  used 
such  expressions  as  the  folio wingf.  "The  threefold 
character  of  the  Universal,  the  Particular,  and  the  Indif- 
ference of  the  two, — as  expressed  in  their  Identity,  is 
Magnetism,  as  expressed  in  their  Difference,  is  Electricity, 
and  as  expressed  in  the  Totality,  is  Chemical  Process. 
Thus  these  forms  are  only  one  form ;  and  the  Chemical 
Process  is  a  mere  transfer  of  the  three  Points  of  Magnet- 
ism into  the  Triangle  of  Chemistry." 

It  was  very  natural  that  the  chemists  should  refuse 
to  acknowledge,  in  this  fanciful  and  vague  language, 
(delivered,  however,  it  is  to  be  recollected,  in  1803,)  an 
anticipation  of  Davy's  doctrine  of  the  identity  of  electrical 
and  chemical  forces,  or  of  (Ersted's  electro-magnetic 
agency.  Yet  it  was  perhaps  no  less  natural  that  the 
author  of  such  assertions  should  look  upon  every  great 
step  in  the  electro-chemical  theory  as  an  illustration 
of  his  own  doctrines.  Accordingly  we  find  Schelling 
welcoming,  with  a  due  sense  of  their  importance,  the  dis- 
coveries of  Faraday.  When  he  heard  of  the  experiment 

*  P.  223?  +  P.  48G, 


358      PHILOSOPHY  OF  THE  MECHANICO-CHEMICAL  SCIENCES. 

in  which  electricity  was  produced  from  common  mag- 
netism, he  fastened  with  enthusiasm  upon  the  discovery, 
even  before  he  knew  any  of  its  details,  and  proclaimed 
it  at  a  public  meeting  of  a  scientific  body*  as  one  of  the 
most  important  advances  of  modern  science.  We  have 
(he  thus  reasoned)  three  effects  of  polar  forces ; — electro- 
chemical Decomposition,  electrical  Action,  Magnetism. 
Volta  and  Davy  had  confirmed  experimentally  the  identity 
of  the  two  former  agencies :  (Ersted  showed  that  a  closed 
voltaic  circuit  acquired  magnetic  properties :  but  in 
order  to  exhibit  the  identity  of  electric  and  magnetic 
action  it  was  requisite  that  electric  forces  should  be 
extricated  from,  magnetic.  This  great  step  Faraday,  he 
remarked,  had  made,  in  producing  the  electric  spark  by 
means  of  magnets. 

13.  Although  conjectures  and  assertions  of  the  kind 
thus  put  forth  by  Schelling  involve  a  persuasion  of  the 
pervading  influence  and  connexion  of  polarities,  which 
persuasion  has  already  been  confirmed  in  many  instances, 
they  involve  this  principle  in  a  manner  so  vague  and 
ambiguous  that  it  can  rarely,  in  such  a  form,  be  of 
any  use  or  value.  Such  views  of  polarity  can  never 
teach  us  in  what  cases  we  are  and  in  what  we  are  not' 
to  expect  to  find  polar  relations  ;  and  indeed  tend  rather 
to  diffuse  error  and  confusion,  than  to  promote  know- 
ledge. Accordingly  we  cannot  be  surprised  to  find  such 
doctrines  put  forward  by  their  authors  as  an  evidence  of 
the  small  value  and  necessity  of  experimental  science. 
This  is  done  by  the  celebrated  metaphysician  Hegel,  in 
his  Encyclopedia^.  "Since,"  says  he,  "the  plane  of 
incidence  and  of  reflection  in  simple  reflection  is  the 
same  plane,  when  a  second  reflector  is  introduced  which 
further  distributes  the  illumination  reflected  from  the 

*  UEBER  FARADAY'S  Neueste  Entdeckung.     Milnchen.    1832. 
f  Sec.  278, 


OF  THE  CONNEXION  OF  POLARITIES.  359 

first,  the  position  of  the  first  plane  with  respect  to  the 
second  plane,  containing  the  direction  of  the  first  reflection 
and  of  the  second,  has  its  influence  upon  the  position, 
illumination  or  darkening  of  the  object  as  it  appears 
by  the  second  reflection.  This  influence  must  be  the 
strongest  when  the  two  planes  are  what  we  must  call 
negatively  related  to  each  other: — that  is,  when  they  are 
at  right  angles."  "  But,"  he  adds,  "  when  men  infer  (as 
Malus  has  done)  from  the  modification  which  is  produced 
by  this  situation,  in  the  illumination  of  the  reflection, 
that  the  molecules  of  light  in  themselves,  that  is,  on  their 
different  sides,  possess  different  physical  energies ;  and 
when  on  this  foundation,  along  with  the  phenomena  of 
entoptical  colours  therewith  connected,  a  wide  labyrinth 
of  the  most  complex  theory  is  erected  ;  we  have  then 
one  of  the  most  remarkable  examples  of  the  inferences  of 
physics  from  experiment."  If  Hegel's  reasoning  prove 
anything,  it  must  prove  that  polarization  always  accom- 
panies reflection  under  such  circumstances  as  he  describes: 
yet  all  physical  philosophers  know  that  in  the  case  of 
metals,  in  which  the  reflection  is  most  complete,  light  is 
not  completely  polarized  at  any  angle ;  and  that  in  other 
substances  the  polarization  depends  upon  various  circum- 
stances which  show  how  idle  and  inapplicable  is  the 
account  he  thus  gives  of  the  property.  His  self-com- 
placent remark  about  the  inferences  of  physics  from 
experiment,  is  intended  to  recommend  by  comparison  his 
own  method  of  considering  the  nature  of  things  in  them- 
selves ;  a  mode  of  obtaining  physical  truth  which  had 
been  more  than  exhausted  by  Aristotle,  and  out  of  which 
no  new  attempts  have  extracted  anything  of  value  since 
his  time. 

14.  Thus  the  general  conclusion  to  which  we  are  led 
on  this  subject  is,  that  the  persuasion  of  the  existence  and 
connexion  or  identity  of  various  polarities  in  nature, 


360      PHILOSOPHY  OF  THE  MECHAN1CO-CHEMICAL  SCIENCES. 

although  very  naturally  admitted,  and  in  many  cases 
interpreted  and  confirmed  by  observed  facts,  is  of  itself, 
so  far  as  we  at  present  possess  it,  a  very  insecure  guide 
to  scientific  doctrines.  When  it  is  allowed  to  dictate 
our  theories,  instead  of  animating  and  extending  our 
experimental  researches,  it  leads  only  to  error,  confusion, 
obscurity,  and  mysticism. 

This  Fifth  Book,  on  the  subject  of  Polarities,  is  a 
short  one  compared  with  most  of  the  others.  This 
arises  in  a  great  measure  from  the  circumstance  that  the 
Idea  of  Polarity  has  only  recently  been  apprehended  and 
applied,  with  any  great  degree  of  clearness,  among  phy- 
sical philosophers ;  and  is  even  yet  probably  entertained 
in  an  obscure  and  ambiguous  manner  by  most  experimental 
inquirers.  I  have  been  desirous  of  not  attempting  to 
bring  forward  any  doctrines  upon  the  subject,  except 
such  as  have  been  fully  illustrated  and  exemplified  by  the 
acknowledged  progress  of  the  physical  sciences.  If  I 
had  been  willing  to  discuss  the  various  speculations 
which  have  been  published  respecting  the  universal  pre- 
valence of  polarities  in  the  universe,  and  their  results  in 
every  province  of  nature,  I  might  easily  have  presented 
this  subject  in  a  more  extended  form ;  but  this  would 
not  have  been  consistent  with  my  plan  of  tracing  the 
influence  of  scientific  ideas  only  so  far  as  they  have  really 
aided  in  disclosing  and  developing  scientific  truths.  And 
as  the  influence  of  this  idea  is  clearly  distinguishable 
both  from  those  which  precede  and  those  which  follow  in 
the  character  of  the  sciences  to  which  it  gives  rise,  and 
appears  likely  to  be  hereafter  of  great  extent  and  conse- 
quence, it  seemed  better  to  treat  of  it  in  a  separate 
Book,  although  of  a  brevity  disproportioned  to  the  rest. 


361 


BOOK  VI. 


THE  PHILOSOPHY  OF  CHEMISTRY. 


CHAPTER  I. 

ATTEMPTS   TO   CONCEIVE  ELEMENTARY 
COMPOSITION. 

1.  WE  have  now  to  bring  into  view,  if  possible,  the 
ideas  and  general  principles  which  are  involved  in  Che- 
mistry,— the  science  of  the  composition  of  bodies.  For  in 
this  as  in  other  parts  of  human  knowledge,  we  shall  find 
that  there  are  certain  ideas,  deeply  seated  in  the  mind, 
though  shaped  and  unfolded  by  external  observation,  which 
are  necessary  conditions  of  the  existence  of  such  a  science. 
These  ideas  it  is  which  impel  man  to  such  a  knowledge 
of  the  composition  of  bodies,  which  give  meaning  to  facts 
exhibiting  this  composition,  and  universality  to  special 
truths  discovered  by  experience.  These  are  the  Ideas  of 
Element  and  of  Substance. 

Unlike  the  idea  of  polarization,  of  which  we  treated 
in  the  last  Book,  these  ideas  have  been  current  in  men's 
minds  from  very  early  times,  and  formed  the  subject  of 
some  of  the  first  speculations  of  philosophers.  It  hap- 
pened however,  as  might  have  been  expected,  that  in  the 
first  attempts  they  were  not  clearly  distinguished  from 
other  notions,  and  were  apprehended  and  applied  in  an 
obscure  and  confused  manner.  We  cannot  better  ex- 
hibit the  peculiar  character  and  meaning  of  these  ideas 
than  by  tracing  the  form  which  they  have  assumed  and 


362  PHILOSOPHY  OF  CHEMISTRY. 

the  efficacy  which  they  have  exerted  in  these  successive 
essays.  This,  therefore,  I  shall  endeavour  to  do,  begin- 
ning with  the  Idea  of  Element. 

2.  That  bodies  are  composed  or  made  up  of  certain 
parts,  elements,  or  principles,  is  a  conception  which  has 
existed  in  men's  minds  from  the  beginning  of  the  first 
attempts  at  speculative  knowledge.  The  doctrine  of  the 
four  elements,  earth,  air,  fire  and  water,  of  which  all 
things  in  the  universe  were  supposed  to  be  constituted,  is 
one  of  the  earliest  forms  in  which  this  conception  was 
systematized;  and  this  doctrine  is  stated  by  various 
authors  to  have  existed  as  early  as  the  times  of  the 
ancient  Egyptians*.  The  words  usually  employed  by 
Greek  writers  to  express  these  elements  are  upx*}>  &  prin- 
ciple or  beginning,  and  o-ro^etov,  which  probably  meant 
a  letter  (of  a  word)  before  it  meant  an  element  of  a 
compound.  For  the  resolution  of  a  word  into  its  letters 
is  undoubtedly  a  remarkable  instance  of  a  successful 
analysis  performed  at  an  early  stage  of  man's  history; 
and  might  very  naturally  supply  a  metaphor  to  denote 
the  analysis  of  substances  into  their  intimate  parts,  when 
men  began  to  contemplate  such  an  analysis  as  a  subject 
of  speculation.  The  Latin  word  elementum  itself,  though 
by  its  form  it  appears  to  be  a  derivative  abstract  term, 
comes  from  some  root  now  obsolete;  probably f  from  a 
word  signifying  to  grow  or  spring  up. 

The  mode  in  which  elements  form  the  compound 
bodies  and  determine  their  properties  was  at  first,  as 
might  be  expected,  vaguely  and  variously  conceived.  It 
will,  I  trust,  hereafter  be  made  clear  to  the  reader  that 
the  relation  of  the  elements  to  the  compound  involves  a 

*  GILBERT'S  Phys.,  1.  i.  c.  3. 

t  Vossius  in  wee.  "  Conjecto  esse  ab  antiqua  voce  eleo  pro  oleo, 
id  est  cresco :  a  qua  significatione  proles,  suboles^  adolescens :  ut  ab 
juratum,  juramentum;  ab  adjutum,  adjumentum:  sic  ab  eletum, 
elementum  :  quia  inde  omnia  crescnnt  ac  nascuntur." 


CONCEPTION  OF  ELEMENTARY  COMPOSITION.  363 

peculiar  and  appropriate  Fundamental  Idea,  not  suscept- 
ible of  being  correctly  represented  by  any  comparison  or 
combination  of  other  ideas,  and  guiding  us  to  clear  and 
definite  results  only  when  it  is  illustrated  and  nourished 
by  an  abundant  supply  of  experimental  facts.  But  at  first 
the  peculiar  and  special  notion  which  is  required  in  a  just 
conception  of  the  constitution  of  bodies  was  neither  dis- 
cerned nor  suspected  ;  and  up  to  a  very  late  period  in  the 
history  of  chemistry,  men  went  on  attempting  to  appre- 
hend the  constitution  of  bodies  more  clearly  by  substitu- 
ting for  this  obscure  and  recondite  idea  of  elementary 
composition,  some  other  idea  more  obvious,  more  lumi- 
nous, and  more  familiar,  such  as  the  ideas  of  resemblance, 
position,  and  mechanical  force.  We  shall  briefly  speak  of 
some  of  these  attempts,  and  of  the  errors  which  were 
thus  introduced  into  speculations  on  the  relations  of 
elements  and  compounds. 

3.  Compounds  assumed  to  resemble  their  Elements. — 
The  first  notion  was  that  compounds  derive  their  qualities 
from  their  elements  by  resemblance: — they  are  hot  in 
virtue  of  a  hot  element,  heavy  in  virtue  of  a  heavy 
element,  and  so  on.  In  this  way  the  doctrine  of  tlivfour 
elements  was  framed;  for  every  body  is  either  hot  or 
cold,  moist  or  dry ;  and  by  combining  these  qualities  in 
all  possible  ways,  men  devised  four  elementary  sub- 
stances, as  has  been  stated  in  the  History*. 

This  assumption  of  the  derivation  of  the  qualities  of 
bodies  from  similar  qualities  in  the  elements  was,  as  we 
shall  see,  altogether  baseless  and  unphilosophical,  yet  it 
prevailed  long  and  universally.  It  was  the  foundation  of 
medicine  for  a  long  period,  both  in  Europe  and  Asia ; 
disorders  being  divided  into  hot,  cold,  and  the  like ;  and 
remedies  being  arranged  according  to  similar  distinctions. 
Many  readers  will  recollect,  perhaps,  the  story f  of  the 

*  Hist.  Ind.  Sri.,  i.  47.  t  See  Hadji  JBaba. 


364  PHILOSOPHY  OF  CHEMISTRY. 

indignation  which  the  Persian  physicians  felt  towards  the 
European,  when  he  undertook  to  cure  the  ill  effects  of 
cucumber  upon  the  patient,  by  means  of  mercurial  medi- 
cine :    for  cucumber,  which  is  cold,  could  not  be  coun- 
teracted, they  maintained,   by  mercury,  which  in  their 
classification  is  cold  also.     Similar  views  of  the  operation 
of  medicines  might  easily  be  traced  in  our  own  country. 
A  moment's  reflection  may  convince  us  that  when  drugs 
of  any   kind    are    subjected    to    the    chemistry    of  the 
human  stomach  and  thus  made  to  operate  on  the  human 
frame,  it  is  utterly  impossible  to  form  the  most  remote 
conjecture  what  the  result  will  be  from  any  such  vague 
notions  of  their   qualities   as   the   common  use  of  our 
senses   can  give.      And   in  like    manner   the   common 
operations  of  chemistry  give  rise  in  almost  every  instance 
to  products  which  bear  no  resemblance  to  the  materials 
employed.     The  results  of  the  furnace,  the  alembic,  the 
mixture  frequently  bear  no   visible  resemblance  to  the 
ingredients  operated  upon.     Iron  becomes  steel  by  the 
addition  of  a  little  charcoal ;    but  what  visible  trace  of 
the  charcoal  is  presented  by  the  metal  thus  modified  ? 
The    most    beautiful    colours    are    given   to   glass    and 
earthenware  by  minute  portions  of  the  ores  of  black  or 
dingy  metals,  as  iron  and  manganese.     The  worker  in 
metal,  the  painter,  the  dyer,    the   vintner,  the  brewer, 
all    the    artisans    in    short    who    deal    with    practical 
chemistry,  are   able   to   teach   the  speculative   chemist 
that  nothing   can   be   so    false    as   to   expect    that  the 
qualities  of  the  elements  shall  be  still  discoverable,  in 
an  unaltered  form,  in  the   compound.     This  first  rude 
notion  of  an  element,  that  it  determines  the  properties 
of  bodies  by  resemblance,  must  be  utterly  rejected  and 
abandoned  before  we  can  make  any  advance  towards  a 
true  apprehension  of  the  constitution  of  bodies. 

4.  This  step  accordingly  was  made,  when  the  hypo- 


CONCEPTION  OF  ELEMENTARY  COMPOSITION.  065 

thesis  of  the  four  elements  was  given  up,  and  the  doctrine 
of  the  three  principles,  salt,  sulphur  and  mercury,  was  sub- 
stituted in  its  place.  For  in  making  this  change,  as  I 
have  remarked  in  the  History*,  the  real  advance  was  the 
acknowledgment  of  the  changes  produced  by  the  chemist's 
operations  as  results  to  be  accounted  for  by  the  union 
and  separation  of  substantial  elements,  however  great 
the  changes,  and  however  unlike  the  product  might  be 
to  the  materials.  And  this  step  once  made,  chemists 
went  on  constantly  advancing  towards  a  truer  view  of 
the  nature  of  an  element,  and  consequently,  towards  a 
more  satisfactory  theory  of  chemical  operations. 

5.  Yet  we  may,  I  think,  note  one  instance,  even  in  the 
works  of  eminent  modem  chemists,  in  which  this  maxim, 
that  we  have  no  right  to  expect  any  resemblance  between 
the  elements  and  the  compound,  is  lost  sight  of.  I  speak 
of  certain  classifications  of  mineral  substances.  Berzelius, 
in  his  System  of  Mineral  Arrangement,  places  sulphur  next 
to  the  sulphurets.  But  surely  this  is  an  error,  involving 
the  ancient  assumption  of  the  resemblance  of  elements 
and  compounds ;  as  if  we  were  to  expect  the  sulphurets 
to  bear  a  resemblance  to  sulphur.  All  classifications  are 
intended  to  bring  together  things  resembling  each  other : 
the  sulphurets  of  metals  have  certain  general  resem- 
blances which  make  them  a  tolerably  distinct,  well 
determined,  class  of  bodies.  But  sulphur  has  no  resem- 
blances with  these,  no  analogies  with  them,  either  in 
physical  or  even  in  chemical  properties.  It  is  a  simple 
body ;  and  both  its  resemblances  and  its  analogies  direct 
us  to  place  it  along  with  other  simple  bodies,  (selenium, 
and  phosphorus,)  which,  united  with  metals,  produce  com- 
pounds not  very  different  from  the  sulphurets.  Sulphur 
cannot  be,  nor  approach  to  being,  a  sulphuret ;  we  must 
not  confound  what  it  is  with  what  it  makes.  Sulphur  has 

*  Hist.  Ind.  Sci.,  iii.  100. 


366  PHILOSOPHY  OF  CHEMISTRY. 

its  proper  influence  in  determining  the  properties  of  the 
compound  into  which  it  enters  ;  but  it  does  not  do  this 
according  to  resemblance  of  qualities,  or  according  to  any 
principle  which  properly  leads  to  propinquity  in  classifi- 
cation. 

6.  Compounds  assumed  to  be  determined  by  the  Figure  of 
Elements. — I  pass  over  the  fanciful  modes  of  representing 
chemical  changes  which  were  employed  by  the  Alche- 
mists ;  for  these  strange  inventions  did  little  in  leading 
men  towards  a  juster  view  of  the  relations  of  elements  to 
compounds.  I  proceed  for  an  instant  to  the  attempt  to 
substitute  another  obvious  conception  for  the  still  obscure 
notion  of  elementary  composition.  It  was  imagined  that 
all  the  properties  of  bodies  and  their  mutual  operations 
might  be  accounted  for  by  supposing  them  constituted  of 
particles  of  various  forms,  round  or  angular,  pointed  or 
hooked,  straight  or  spiral.  This  is  a  very  ancient  hypo- 
thesis, and  a  favourite  one  with  many  casual  speculators 
in  all  ages.  Thus  Lucretius  undertakes  to  explain  why 
wine  passes  rapidly  through  a  sieve  and  oil  slowly,  by 
telling  us  that  the  latter  substance  has  its  particles  either 
larger  than  those  of  the  other,  or  more  hooked  and  inter- 
woven together.  And  he  accounts  for  the  difference  of 
sweet  and  bitter  by  supposing  the  particles  in  the  former 
case  to  be  round  and  smooth,  in  the  latter  sharp  and 
jagged*.  Similar  assumptions  prevailed  in  modern  times 
on  the  revival  of  the  mechanical  philosophy,  and  consti- 
tute a  large  part  of  the  physical  schemes  of  Descartes 
and  Gassendi.  They  were  also  adopted  to  a  considerable 
extent  by  the  chemists.  Acids  were  without  hesitation 
assumed  to  consist  of  sharp  pointed  particles;  which,  "I 
hope,"  Lemery  saysf,  "  no  one  will  dispute,  seeing  every 
one's  experience  does  demonstrate  it :  he  needs  but  taste 
an  acid  to  be  satisfied  of  it,  for  it  pricks  the  tongue  like 

*  De  Rerum  Natura,  ii.  390  sqq.  t  Chemistry,  p.  25. 


CONCEPTION  OF  ELEMENTARY  COMPOSITION.  367 

anything  keen  and  finely  cut."  Such  an  assumption  is 
not  only  altogether  gratuitous  and  useless,  but  appears  to 
be  founded  in  some  degree  upon  a  confusion  in  the  meta- 
phorical and  literal  use  of  such  words  as  keen  and  sharp. 
The  assumption  once  made,  it  was  easy  to  accommodate 
it,  in  a  manner  equally  arbitrary,  to  other  facts.  "A 
demonstrative  and  convincing  proof  that  an  acid  does 
consist  of  pointed  parts  is,  that  not  only  all  acid  salts  do 
crystallize  into  edges,  but  all  dissolutions  of  different 
things,  caused  by  acid  liquors,  do  assume  this  figure  in 
their  crystallization.  These  crystals  consist  of  points 
differing  both  in  length  and  bigness  one  from  another, 
and  this  diversity  must  be  attributed  to  the  keener  or 
blunter  edges  of  the  different  sorts  of  acids :  and  so  like- 
wise this  difference  of  the  points  in  subtilty  is  the  cause 
that  one  acid  can  penetrate  and  dissolve  with  one  sort  of 
miivt,  that  another  can't  rarify  at  all :  Thus  vinegar  dis- 
solves lead,  which  aquafortis  can't :  aqua  fortis  dissolves 
quicksilver,  which  vinegar  will  not  touch ;  aqua  regalis 
dissolves  gold,  whenas  aquafortis  cannot  meddle  with  it; 
on  the  contrary,  aqua  fortis  dissolves  silver,  but  can  do 
nothing  with  gold,  and  so  of  the  rest." 

The  leading  fact  of  the  vehement  combination  and 
complete  union  of  acid  and  alkali  readily  suggested  a  fit 
form  for  the  particles  of  the  latter  class  of  substances. 
"  This  effect,"  Lemery  adds,  "  may  make  us  reasonably 
conjecture  that  an  alkali  is  a  terrestrious  and  solid  matter 
whose  forms  are  figured  after  such  a  manner  that  the 
acid  points  entering  in  do  strike  and  divide  whatever 
opposes  their  motion."  And  in  a  like  spirit  are  the 
speculations  in  Dr.  MEAD'S  Mechanical  Account  of  Poisons 
(1745).  Thus  he  explains  the  poisonous  effect  of  corrosive 
sublimate  of  mercury  by  saying*  that  the  particles  of  the 
salt  are  a  kind  of  lamellae  or  blades  to  which  the 

*  P.  199. 


368  PHILOSOPHY  OF  CHEMISTRY. 

mercury  gives  an  additional  weight.  If  resublimed  with 
three-fourths  the  quantity  of  mercury,  it  loses  its  corro- 
siveness,  (becoming  calomel,)  which  arises  from  this,  that 
in  sublimation  "  the  crystalline  blades  are  divided  every 
time  more  and  more  by  the  force  of  the  fire  ;"  and  "  the 
broken  pieces  of  the  crystals  uniting  into  little  masses  of 
differing  figures  from  their  former  make,  those  cutting 
points  are  now  so  much  smaller  that  they  cannot  make 
wounds  deep  enough  to  be  equally  mischievous  and 
deadly :  and  therefore  do  only  vellicate  and  twitch  the 
sensible  membranes  of  the  stomach." 

7.  Among  all  this  very  fanciful  and  gratuitous  assump- 
tion we  may  notice  one  true  principle  clearly  introduced, 
namely,  that  the  suppositions  which  we  make  respecting 
the  forms  of  the  elementary  particles  of  bodies  and  their 
mode  of  combination  must  be  such  as  to  explain  the  facts 
of  crystallization,  as  well  as  of  mere  chemical  change. 
This  principle  we  shall  hereafter  have  occasion  to  insist 
upon  further. 

I  now  proceed  to  consider  a  more  refined  form  of 
assumption  respecting  the  constitution  of  bodies,  yet  still 
one  in  which  a  vain  attempt  is  made  to  substitute  for  the 
peculiar  idea  of  chemical  composition  a  more  familiar 
mechanical  conception. 

8.  Compounds  assumed  to  be  determined  by  the  Mecha- 
nical Attraction  of  the  Elements. — When,  in  consequence 
of  the  investigations  and  discoveries  of  Newton  and  his 
predecessors,  the  conception    of  mechanical   force   had 
become  clear  and  familiar,  so  far  as  the  action  of  external 
forces  upon  a  body  was  concerned,  it  was  very  natural 
that  the  mathematicians  who  had  pursued  this  train  of 
speculation  should  attempt  to  apply  the  same  conception 
to  that  mutual  action  of  the  internal  parts  of  a  body  by 
which  they  are  held  together.      Newton    himself  had 
pointed  the  way  to  this  attempt.     In  the  Preface  to  the 


CONCEPTION  OF  ELEMENTARY  COMPOSITION.  369 

Principia,  after  speaking  of  what  he  has  done  in  calcu- 
lating the  effects  of  forces  upon  the  planets,  satellites, 
&c.,  he  adds,  "  Would  it  were  permitted  us  to  deduce  the 
other  phenomena  of  nature  from  mechanical  principles 
by  the  same  kind  of  reasoning.  For  many  things  move 
me  to  suspect  that  all  these  phenomena  depend  upon 
certain  forces,  by  which  the  particles  of  bodies,  through 
causes  not  yet  known,  are  either  urged  towards  each 
other,  and  cohere  according  to  regular  figures,  or  are 
repelled  and  recede  from  each  other ;  which  forces  being 
unknown,  philosophers  have  hitherto  made  their  attempts 
upon  nature  in  vain."  The  same  thought  is  at  a  later 
period  followed  out  further  in  one  of  the  Queries  at  the 
end  of  the  Opticks*.  "  Have  not  the  small  particles  of 
bodies  certain  Powers,  Virtues,  or  Forces  by  which  they 
act  at  a  distance,  not  only  upon  the  rays  of  light  for 
reflecting,  refracting  and  inflecting  them,  but  also  upon 
one  another  for  producing  a  great  part  of  the  phenomena 
of  nature?"  And  a  little  further  on  he  proceeds  to 
apply  this  expressly  to  chemical  changes.  "  When  Salt 
of  Tartar  runs  per  deliquium  [or  as  we  now  express  it, 
deliquesces]  is  not  this  done  By  an  attraction  between  the 
particles  of  the  Salt  of  Tartar  and  the  particles  of  the 
water  which  float  in  the  air  in  the  form  of  vapours  ? 
And  why  does  not  common  salt,  or  saltpetre,  or  vitriol, 
run  per  deliquium,  but  for  want  of  such  an  attraction  ?  or 
why  does  not  Salt  of  Tartar  draw  more  water  out  of  the 
air  than  in  a  certain  proportion  to  its  quantity,  but  for 
want  of  an  attractive  force  after  it  is  saturated  with 
water  ?"  He  goes  on  to  put  a  great  number  of  similar 
cases,  all  tending  to  the  same  point,  that  chemical  com- 
binations cannot  be  conceived  in  any  other  way  than  as 
an  attraction  of  particles. 

9.  Succeeding  speculators  in  his  school  attempted  to 

*  Query  31. 
VOL.  I.  2  B 


370  PHILOSOPHY  OF  CHEMISTRY. 

follow  out  this  view.  Dr.  Frend,  of  Christ  Church,  in 
1710,  published  his  Prcelectiones  Gliymica,  in  quibusomnes 
fere  Operationes  Vliymicce  ad  vera  Principia  ex  ipsius 
Natures  Legibus  rediguntur.  Oxonii  habita.  This  book  is 
dedicated  to  Newton,  and  in  the  dedication,  the  promise 
of  advantage  to  chemistry  from  the  influence  of  the 
Newtonian  discoveries  is  spoken  of  somewhat  largely, — 
much  more  largely,  indeed,  than  has  yet  been  justified  by 
the  sequel.  After  declaring  in  strong  terms  that  the 
only  prospect  of  improving  science  consists  in  following 
the  footsteps  of  Newton,  the  author  adds,  "  That  force 
of  attraction,  of  which  you  first  so  successfully  traced 
the  influence  in  the  heavenly  bodies,  operates  in  the  most 
minute  corpuscles,  as  you  long  ago  hinted  in  your  Prin- 
cipia, and  have  lately  plainly  shown  in  your  Opticks ; 
and  this  force  we  are  only  just  beginning  to  perceive  and 
to  study.  Under  these  circumstances  I  have  been  desir- 
ous of  trying  what  is  the  result  of  this  view  in  chemistry." 
The  work  opens  formally  enough,  with  a  statement  of 
general  mechanical  principles,  of  which  the  most  peculiar 
are  these  : — That  there  exists  an  attractive  force  by  which 
particles  when  at  very  small  distances  from  each  other, 
are  drawn  together ; — that  this  force  is  different,  accord- 
ing to  the  different  figure  and  density  of  the  particles ; 
— that  the  force  may  be  greater  on  one  side  of  a  par- 
ticle than  on  the  other ; — that  the  force  by  which  par- 
ticles cohere  together  arises  from  attraction,  and  is  vari- 
ously modified  according  to  the  quantity  of  contacts." 
But  these  principles  are  not  applied  in  any  definite 
manner  to  the  explanation  of  specific  phenomena.  He 
attempts,  indeed,  the  question  of  special  solvents*.  Why 
does  aqua  fortis  dissolve  silver  and  not  gold,  while  aqua 
regia  dissolves  gold  and  not  silver?  which,  he  says,  is 
the  most  difficult  question  in  chemistry,  and  which  is 

*  P.  54. 


CONCEPTION  OF  ELEMENTARY  COMPOSITION.          371 

certainly  a  fundamental  one  in  the  formation  of  chemical 
theory.  He  solves  it  by  certain  assumptions  respecting 
the  forces  of  attraction  of  the  particles,  and  also  the 
diameter  of  the  particles  of  the  acids  and  the  pores  of 
the  metals,  all  which  suppositions  are  gratuitous. 

10.  We  may  observe  further,  that  by  speaking,  as  I  have 
stated  that  he  does,  of  the  figure  of  particles,  he  mixes  to- 
gether the  assumption  of  the  last  section  with  the  one 
which  we  are  considering  in  this.  This  combination  is  very 
unphilosophical,  or,  to  say  the  least,  very  insufficient,  since 
it  makes  a  new  hypothesis  necessary.  If  a  body  be  com- 
posed of  cubical  particles,  held  together  by  their  mutual 
attraction,  by  what  force  are  the  parts  of  each  cube  held 
together?  In  order  to  understand  their  structure,  we 
are  obliged  again  to  assume  a  cohesive  force  of  the 
second  order,  binding  together  the  particles  of  each 
particle.  And  therefore  Newton  himself  says*,  .very 
justly,  "  The  parts  of  all  homogeneal  hard  bodies  which 
fully  touch  each  other,  stick  together  very  strongly :  and 
for  explaining  how  this  is,  some  have  invented  hooked 
atoms,  which  is  begging  the  question"  For  (he  means 
to  imply,)  how  do  the  parts  of  the  hook  stick  together  ? 

The  same  remark  is  applicable  to  all  hypotheses  in 
which  particles  of  a  complex  structure  are  assumed  as  the 
constituents  of  bodies  :  for  while  we  suppose  bodies  and 
their  known  properties  to  result  from  the  mutual  actions 
of  these  particles,  we  are  compelled  tJ  suppose  the  parts 
of  each  particle  to  be  held  together  by  forces  still  more 
difficult  to  conceive,  since  they  are  disclosed  only  by  the 
properties  of  these  particles,  which  as  yet  are  unknown. 
Yet  Newton  himself  has  not  abstained  from  such  hypo- 
theses :  thus  he  saysf,  "  A  particle  of  a  salt  may  be  com- 
pared to  a  chaos,  being  dense,  hard,  dry,  and  earthy  in  the 
centre,  and  moist  and  watery  in  the  circumference." 

*  Opticks,  p.  364.  t  Ib.,  p.  362. 

2  B  2 


372  PHILOSOPHY  OF  CHEMISTRY. 

Since  Newton's  time  the  use  of  the  term  attrac- 
tion, as  expressing  the  cause  of  the  union  of  the 
chemical  elements  of  bodies,  has  been  familiarly  con- 
tinued; and  has,  no  doubt,  been  accompanied  in  the 
minds  of  many  persons  with  an  obscure  notion  that 
chemical  attraction  is,  in  some  way,  a  kind  of  mechanical 
attraction  of  the  particles  of  bodies.  Yet  this  view  has 
never,  so  far  as  I  am  aware,  been  worked  out  into  a 
system  of  chemical  theory;  nor  even  applied  with  any 
distinctness  as  an  explanation  of  any  particular  chemical 
phenomena.  Any  such  attempt,  indeed,  could  only  tend 
to  bring  more  clearly  into  view  the  entire  inadequacy  of 
such  a  mode  of  explanation.  For  the  leading  pheno- 
mena of  chemistry  are  all  of  such  a  nature  that  no 
mechanical  combination  can  serve  to  express  them,  with- 
out an  immense  accumulation  of  additional  hypotheses. 
If  we  take  as  our  problem  the  changes  of  colour, 
transparency,  texture,  taste,  odour,  produced  by  small 
changes  in  the  ingredients,  how  can  we  expect  to 
give  a  mechanical  account  of  these,  till  we  can  give 
a  mechanical  account  of  colour,  transparency,  texture, 
taste,  odour,  themselves  ?  And  if  our  mechanical  hypo- 
thesis of  the  elementary  constitution  of  bodies  does  not 
explain  such  phenomena  as  those  changes,  what  can  it 
explain,  or  what  can  be  the  value  of  it?  I  do  not  here 
insist  upon  a  remark  which  will  afterwards  come  before 
us,  that  even  crystalline  form,  a  phenomenon  of  a  far 
more  obviously  mechanical  nature  than  those  just  alluded 
to,  has  never  yet  been  in  any  degree  explained  by  such 
assumptions  as  this,  that  bodies  consist  of  elementary 
particles  exerting  forces  of  the  same  nature  as  the  central 
forces  which  we  contemplate  in  Mechanics. 

When  therefore  Newton  asks,  "  When  some  stones, 
as  spar  of  lead,  dissolved  in  proper  menstruums,  become 
salts,  do  not  these  things  show  that  salts  are  dry  earth 


CONCEPTION  OF  ELEMENTARY  COMPOSITION.  373 

and  watery  acid  united  by  attraction  f  "  we  may  answer, 
that  this  mode  of  expression  appears  to  be  intended  to 
identify  chemical  combination  with  mechanical  attrac- 
tion ; — that  there  would  be  no  objection  to  any  such 
identification  if  we  could,  in  that  way,  explain,  or  even 
classify  well,  a  collection  of  chemical  facts ;  but  that 
this  has  never  yet  been  done  by  the  help  of  such  expres- 
sions. Till  some  advance  of  this  kind  can  be  pointed 
out,  we  must  necessarily  consider  the  power  which  pro- 
duces chemical  combination  as  a  peculiar  principle,  a 
special  relation  of  the  elements,  not  rightly  expressed  in 
mechanical  terms.  And  we  now  proceed  to  consider  this 
relation  under  the  name  by  which  it  is  most  familiarly 
known. 

CHAPTER  II. 

ESTABLISHMENT  AND  DEVELOPMENT  OF  THE 
IDEA  OF  CHEMICAL  AFFINITY. 

1.  THE  earlier  chemists  did  not  commonly  involve 
themselves  in  the  confusion  into  which  the  mechanical 
philosophers  ran,  of  comparing  chemical  to  mechanical 
forces.  Their  attention  was  engaged,  and  their  ideas 
were  moulded,  by  their  own  pursuits.  They  saw  that  the 
connexion  of  elements  and  compounds  with  which  they 
had  to  deal,  was  a  peculiar  relation  which  must  be  studied 
directly;  and  which  must  be  understood,  if  understood 
at  all,  in  itself,  and  not  by  comparison  with  a  dif- 
ferent class  of  relations.  At  different  periods  of  the 
progress  of  chemistry,  the  conception  of  this  relation, 
still  vague  and  obscure,  was  expressed  in  various  man- 
ners; and  at  last  this  conception  was  clothed  in  tole- 
rably consistent  phraseology,  and  the  principles  which  it 
involved  were,  by  the  united  force  of  thought  and  expe- 
riment, brought  into  view. 


374  PHILOSOPHY  OF  CHEMISTRY. 

2.  The  power  by  which  the  elements  of  bodies  com- 
bine chemically,  being,  as  we  have  seen,  a  peculiar  agency, 
different  from  mere  mechanical  connexion  or  attraction, 
it  is  desirable  to  have  it  designated  by  a  distinct  and 
peculiar  name  ;  and  the  term  affinity  has  been  employed 
for  that  purpose  by  most  modern  chemists.  The  word 
"  affinity"  in  common  language  means,  sometimes  resem- 
blance, and  sometimes  relationship  and  ties  of  family. 
It  is  from  the  latter  sense  that  the  metaphor  is  bor- 
rowed when  we  speak  of  chemical  affinity.  By  the 
employment  of  this  term  we  do  not  indicate  resemblance, 
but  disposition  to  unite.  Using  the  word  in  a  common 
unscientific  manner,  we  might  say  that  chlorine,  bromine, 
and  iodine  have  a  great  natural  affinity  with  each  other, 
for  there  are  considerable  resemblances  and  analogies 

o 

among  them ;  but  these  bodies  have  very  little  chemical 
affinity  for  each  other.  The  use  of  the  word  in  the 
former  sense,  of  resemblance,  can  be  traced  in  earlier 
chemists;  but  it  does  not  appear  to  have  acquired  its 
peculiar  chemical  meaning  till  after  Boerhaave's  time. 
Boerhaave,  however,  is  the  writer  in  whom  we  first  find 
a  due  apprehension  of  the  peculiarity  and  importance 
of  the  Idea  which  it  now  expresses.  When  we  make 
a  chemical  solution*,  he  says,  not  only  are  the  particles 
of  the  dissolved  body  separated  from  each  other,  but 
they  are  closely  united  to  the  particles  of  the  solvent. 
When  aqua  regia  dissolves  gold,  do  you  not  see,  he  says 
to  his  hearers,  that  there  must  be  between  each  particle 
of  the  solvent  and  of  the  metal,  a  mutual  virtue  by  which 
each  loves,  unites  with,  and  holds  the  other  (amat,  unity 
retinet)  ?  The  opinion  previously  prevalent  had  been  that 
the  solvent  merely  separates  the  parts  of  the  body  dis- 
solved :  and  most  philosophers  had  conceived  this  separa- 
tion as  performed  by  mechanical  operations  of  the  par- 
*  Elementa  Chemice.  Lugd.  Bat.  1732,  p.  677. 


IDEA    OF    CHEMICAL    AFFINITY.  375 

tides,  resembling,  for  instance,  the  operation  of  wedges 
breaking  up  a  block  of  timber.  But  Boerhaave  forcibly 
and  earnestly  points  out  the  insufficiency  of  the  concep- 
tion. This,  he  says,  does  not  account  for  what  we  see. 
We  have  not  only  a  separation,  but  a  new  combination. 
There  is  a  force  by  which  the  particles  of  the  solvent 
associate  to  themselves  the  parts  dissolved,  not  a  force  by 
which  they  repel  and  dissever  them.  We  are  here  to 
imagine  not  mechanical  action,  not  violent  impulse,  not 
antipathy,  but  love,  at  least  if  love  be  the  desire  of  unit- 
ing. (Non  igitur  hie  etiam  actiones  mechanicae,  non 
propulsiones  violentae,  non  inimicitiae  cogitandae,  sed 
amicitiae,  si  amor  dicendus  copulas  cupido.)  The  novelty 
of  this  view  is  evidenced  by  the  mode  in  which  he  apolo- 
gizes for  introducing  it.  "  Fateor,  paradoxa  haec  assertio." 
To  Boerhaave,  therefore,  (especially  considering  his  great 
influence  as  a  teacher  of  chemistry,)  we  may  assign  the 
merit  of  first  diffusing  a  proper  view  of  chemical  affinity 
as  a  peculiar  force,  the  origin  of  almost  all  chemical 
changes  and  operations. 

3.  To  Boerhaave  is  usually  assigned  also  the  credit  of 
introducing  the  word  "  affinity"  among  chemists ;  but  I  do 
not  find  that  the  word  is  often  used  by  him  in  this  sense ; 
perhaps  not  at  all*.  But  however  this  may  be,  the  term  is 

*  See  DUMAS,  Legons  de  Philos.  Chim.,  p.  364.  REES'  Cyclopaedia, 
Art.  Chemistry.  In  the  passage  of  Boerhaave  to  which  I  refer  above, 
affinitas  is  rather  opposed  to,  than  identified  with,  chemical  combina- 
tion. When,  he  says,  the  parts  of  the  body  to  be  dissolved  are 
dissevered  by  the  solvent,  why  do  they  remain  united  to  the  particles 
of  the  solvent,  and  why  do  not  rather  both  the  particles  of  the  solvent 
and  of  the  dissolved  body  collect  into  homogeneous  bodies  by  their 
affinity  ?  denuo  se  affinitate  suse  nature  colligant  in  corpora  homo- 
genea  ?  And  the  answer  is,  because  they  possess  another  force  which 
counteracts  this  affinity  of  homogeneous  particles,  and  makes  com- 
pounds of  different  elements.  Affinity,  in  chemistry,  now  means  the 
tendency  of  different  kinds  of  matter  to  unite:  but  it  appears,  as  I 
have  said,  to  have  acquired  this  sense  since  Boerhaave's  time. 


376  PHILOSOPHY   OF   CHEMISTRY. 

on  many  accounts  well  worthy  to  be  preserved,  as  I  shall 
endeavour  to  show.  Other  terms  were  used  in  the  same 
sense  during  the  early  part  of  the  eighteenth  century. 
Thus  when  Geoffroy,  in  1718,  laid  before  the  Academy 
of  Paris  his  Tables  of  Affinities,  which  perhaps  did  more 
than  any  other  event  to  fix  the  idea  of  affinity,  he  termed 
them  "  Tables  of  the  Relations  of  Bodies ;"  "  Tables  des 
Rapports :"  speaking  however,  also,  of  their  "  disposition 
to  unite,"  and  using  other  phrases  of  the  same  import. 

The  term  attraction,  having  been  recommended  by 
Newton  as  a  fit  word  to  designate  the  force  which  pro- 
duces chemical  combination,  continued  in  great  favour  in 
England,  where  the  Newtonian  philosophy  was  looked 
upon  as  applicable  to  every  branch  of  science.  In  France, 
on  the  contrary,  where  Descartes  stilt  reigned  triumphant, 
"  attraction,"  the  watch-word  of  the  enemy,  was  a  sound 
never  uttered  but  with  dislike  and  suspicion.  In  1718 
(in  the  notice  of  Geoffrey's  Tables,)  the  Secretary  of  the 
Academy,  after  pointing  out  some  of  the  peculiar  circum- 
stances of  chemical  combinations  says,  "  Sympathies  and 
attractions  would  suit  well  here,  if  there  were  such 
things."  "  Les  sympathies,  les  attractions  conviendroient 
bien  ici,  si  elles  etaient  quelque  chose."  And  at  a  later 
period,  in  1731,  having  to  write  the  eloge  of  Geoffroy 
after  his  death,  he  says,  "He  gave,  in  1718,  a  singular 
system,  and  a  Table  of  Affinities,  or  Relations  of  the 
different  substances  in  chemistry.  These  affinities  gave 
uneasiness  to  some  persons,  who  feared  that  they  were 
attractions  in  disguise,  and  all  the  more  dangerous  in  con- 
sequence of  the  seductive  forms  which  clever  people  have 
contrived  to  give  them.  It  was  found  in  the  sequel  that 
this  scruple  might  be  got  over." 

This  is  the  earliest  published  instance,  so  far  as  I  am 
aware,  in  which  the  word  "affinity"  is  distinctly  used  for  the 
cause  of  chemical  composition ;  and  taking  into  account 


IDEA  OF  CHEMICAL  AFFINITY.  377 

the  circumstances,  the  word  appears  to  have  been  adopted 
in  France  in  order  to  avoid  the  word  attraction,  which 
had  the  taint  of  Newtonianism.  Accordingly  we  find 
the  word  ajffinite  employed  in  the  works  of  French  che- 
mists from  this  time.  Thus,  in  the  Transactions  of  the 
French  Academy  for  1746,  in  a  paper  of  Macquer's  upon 
Arsenic,  he  says*,  "  On  peut  facilement  rendre  raison  de 
ces  phenomenes  par  le  moyen  des  affinites  que  les  dif- 
ferens  substances  qui  entrent  dans  ces  combinaisons,  ont 
les  uns  avec  les  autres :"  and  he  proceeds  to  explain  the 
facts  by  reference  to  Geoffrey's  Table.  And  in  Macquer's 
Elements  of  Chemistry,  which  appeared  a  few  years  later, 
the  "  affinity  of  composition "  is  treated  of  as  a  leading 
part  of  the  subject,  much  in  the  same  way  as  has  been 
practised  in  such  books  up  to  the  present  time.  From 
this  period  the  word  appears  to  have  become  familiar  to 
all  European  chemists  in  the  sense  of  which  we  are  now 
speaking.  Thus,  in  the  year  1758,  the  Academy  of 
Sciences  at  Rouen  offered  a  prize  for  the  best  dissertation 
on  Affinity.  The  prize  was  shared  between  M.  Limbourg 
of  Theux,  near  Liege,  and  M.  Le  Sage  of  Geneva f. 
About  the  same  time  other  persons  (Manherrj:,  Nicolai$, 
and  others)  wrote  on  the  same  subject,  employing  the 
same  name. 

Nevertheless,  in  1775,  the  Swedish  chemist  Bergman, 
pursuing  still  further  this  subject  of  chemical  affinities, 
and  the  expression  of  them  by  means  of  tables,  returned 
again  to  the  old  Newtonian  term;  and  designated  the 
disposition  of  a  body  to  combine  with  one  rather  than 

*  A.  P.  1746,  p.  201. 

t  THOMSON'S   Chemistry,  iii.   10.      Limbourg's  Dissertation   was 
published  at  Liege,  in  1761 ;  and  Le  Sage's  at  Geneva. 
J  Dissertatio  de  Affinitate  Corporum.     Vindob.  1762. 
§  Progr.   I.  II.    de  Affinitate  Corporum  Chimica.       Jen.   1775, 

1776. 


378  PHILOSOPHY  OF  CHEMISTRY. 

another  of  two  others  as  elective  attraction.  And  as  his 
work  on  Elective  Attractions  had  great  circulation  and 
great  influence,  this  phrase  has  obtained  a  footing  by  the 
side  of  affinity,  and  both  one  arid  the  other  are  now  in 
common  use  among  chemists. 

4.  I  have  said  above  that  the  term  Affinity  is  worthy 
of  being  retained  as  a  technical  term.  If  we  use  the 
word  attraction  in  this  case,  we  identify  or  compare 
chemical  with  mechanical  attraction ;  from  which  iden- 
tification and  comparison,  as  I  have  already  remarked, 
no  one  has  yet  been  able  to  extract  the  means  of  ex- 
pressing any  single  scientific  truth.  If  such  an  identifi- 
cation or  comparison  be  not  intended,  the  use  of  the 
same  word  in  two  different  senses  can  only  lead  to  con- 
fusion :  and  the  proper  course,  recommended  by  all  the 
best  analogies  of  scientific  history,  is  to  adopt  a  peculiar 
term  for  that  peculiar  relation  on  which  chemical  com- 
position depends.  The  word  affinity,  even  if  it  were  not 
rigorously  proper  according  to  its  common  meaning, 
still,  being  simple,  familiar,  and  well  established  in  this 
very  usage,  is  much  to  be  preferred  before  any  other. 

But  further,  there  are  some  analogies  drawn  from 
the  common  meaning  of  this  word,  which  appear  to 
recommend  it  as  suitable  for  the  office  which  it  has 
to  discharge.  For  common  mechanical  attractions  and 
repulsions,  the  forces  by  which  one  body  considered  as  a 
whole  acts  upon  another  external  to  it,  are,  as  we  have 
said,  to  be  distinguished  from  those  more  intimate  ties 
by  which  the  parts  of  each  body  are  held  together.  Now 
this  difference  is  implied,  if  we  compare  the  former  rela- 
tions, the  attractions  and  repulsions,  to  alliances  and  wars 
between  states,  and  the  latter,  the  internal  union  of  parti- 
cles, to  those  bonds  of  affinity  which  connect  the  citizens 
of  the  same  state  with  one  another,  and  especially  to  the 
ties  of  family.  We  have  seen  that  Boerhaave  compares 


IDEA  OF  CHEMICAL  AFFINITY.  379 

the  union  of  two  elements  of  a  compound  to  their  mar- 
riage; "we  must  allow,"  says  an  eminent  chemist  of 
our  own  time*,  "  that  there  is  some  truth  in  this  poetical 
comparison."  It  contains  this  truth,  that  the  two 
become  one  to  most  intents  and  purposes,  and  that  the 
unit  thus  formed  (the  family)  is  not  a  mere  juxtaposition 
of  the  component  parts.  And  thus  the  idea  of  Affinity  as 
the  peculiar  principle  of  chemical  composition,  is  esta- 
blished among  chemists,  and  designated  by  a  familiar  and 
appropriate  name. 

5.  Analysis  is  possible. — We  must,  however,  endea- 
vour to  obtain  a  further  insight  into  this  idea,  thus  fixed 
and  named.  We  must  endeavour  to  extricate,  if  not 
from  the  idea  itself,  from  the  processes  by  which  it  has 
obtained  acceptation  and  currency  among  chemists,  some 
principles  which  may  define  its  application,  some  addi- 
tional specialties  in  the  relations  which  it  implies.  This 
we  shall  proceed  to  do. 

The  idea  of  affinity,  as  already  explained,  implies  a 
disposition  to  combine.  But  this  combination  is  to  be 
understood  as  admitting  also  of  a  possibility  of  separa- 
tion. Synthesis  implies  analysis  as  conceivable :  or  to 
recur  to  the  image  which  we  have  already  used,  divorce 
is  possible  when  the  marriage  has  taken  place. 

That  there  is  this  possibility,  is  a  conviction  implied  in 
all  the  researches  of  chemists,  ever  since  the  true  notion  of 
composition  began  to  predominate  in  their  investigations. 
One  of  the  first  persons  who  clearly  expressed  this  con- 
viction was  Mayow,  an  English  physician,  who  published 
his  Medico-Physical  Tracts  in  1674.  The  first  of  them, 
De  Sale-Nitro  et  Spiritu  Nitro-Aerio,  contains  a  clear 
enunciation  of  this  principle.  After  showing  how,  in  the 
combinations  of  opposite  elements,  as  acid  and  alkali, 
their  properties  entirely  disappear,  and  a  new  substance 
*  DUMAS,  Lemons  de  Phil.  Chim.,  p.  363. 


380        .  PHILOSOPHY  OF  CHEMISTRY. 

is  formed  not  at  all  resembling  either  of  the  ingredients, 
he  adds*,  "Although  these  salts  thus  mixed  appear  to  be 
destroyed,  it  is  still  possible  for  them  to  be  separated 
from  each  other,  with  their  powers  still  entire."  He 
proceeds  to  exemplify  this,  and  illustrates  it  by  the  same 
image  which  I  have  already  alluded  to :  "  Salia  acida  a 
salibus  volatilibus  discedunt,  ut  cum  sale  fixo  tartari, 
tanquam  sponso  magis  idoneo,  conjugium  strictius  ineunt." 
This  idea  of  a  synthesis  which  left  a  complete  analysis  still 
possible,  was  opposed  to  a  notion  previously  current,  that 
when  two  heterogeneous  bodies  united  together  and 
formed  a  third  body,  the  two  constituents  were  entirely 
destroyed,  and  the  result  formed  out  of  their  ruinsf- 
And  this  conception  of  synthesis  and  analysis,  as  processes 
which  are  possible  successively  and  alternately,  and  each 
of  which  supposes  the  possibility  of  the  other,  has  been 
the  fundamental  and  regulative  principle  of  the  operations 
and  speculations  of  analytical  chemistry  from  the  time  of 
Mayow  to  the  present  day. 

6.  Affinity  is  elective. — When  the  idea  of  chemical 
affinity,  or  disposition  to  unite,  was  brought  into  view  by 
the  experiments  and  reasonings  of  chemists,  they  found 
it  necessary  to  consider  this  disposition  as  elective; — 
each  element  chose  one  rather  than  another  of  the  ele- 
ments which  were  presented  to  it,  and  quitted  its  union 
with  one  to  unite  with  another  which  it  preferred.  This 
has  already  appeared  in  the  passage  just  quoted  from 
Mayow.  He  adds  in  the  same  strain,  "  I  have  no  doubt 
that  fixed  salts  choose  one  acid  rather  than  another,  in 
order  that  they  may  coalesce  with  it  in  a  more  intimate 
union." — "  Nullus  dubito  salia  fixa  acidum  unum  prse 
aliis  eligere,  ut  cum  eodem  arctiore  unione  coalescant." 
The  same  thought  is  expressed  and  exemplified  by  other 
chemists :  they  notice  innumerable  cases  in  which,  when 

*  Cap.  xiv.,  p.  233.  t  THOMSON'S  Chemistry,  iii.  8. 


IDEA  OF  CHEMICAL  AFFINITY.  381 

an  ingredient  is  combined  with  a  liquid,  if  a  new  sub- 
stance be  immersed  which  has  a  greater  affinity  for  the 
liquid,  the  liquid  combines  with  the  new  substance  by 
election,  and  the  former  ingredient  is  precipitated.  Thus 
Stahl  says*,  "In  spirit  of  nitre  dissolve  silver;  put  in 
copper  and  the  silver  is  thrown  down ;  put  in  iron  and 
the  copper  goes  down ;  put  in  zinc,  the  iron  precipitates ; 
put  in  volatile  alkali,  the  zinc  is  separated ;  put  in  fixed 
alkali,  the  volatile  quits  its  hold." — As  may  be  seen  in 
this  example,  we  have  in  such  cases,  not  only  a  prefer- 
ence, but  a  long  gradation  of  preferences.  The  spirit  of 
nitre  will  combine  with  silver,  but  it  prefers  copper; 
prefers  iron  more;  zinc  still  more;  volatile  alkali  yet 
more ;  fixed  alkali  the  most. 

The  same  thing  was  proved  to  obtain  with  regard  to 
each  element ;  and  when  this  was  ascertained,  it  became 
the  object  of  chemists  to  express  these  degrees  of  prefer- 
ence, by  lists  in  which  substances  were  arranged  accord- 
ing to  their  disposition  to  unite  with  another  substance. 
In  this  manner  was  formed  Geoffrey's  Table  of  Affinities 
(1718),  which  we  have  already  mentioned.  This  Table 
was  further  improved  by  other  writers,  as  Gellert  (1751) 
and  Limbo urg  (1761).  Finally  Bergman  improved  these 
Tables  still  further,  taking  into  account  not  only  the 
order  of  affinities  of  each  element  for  others,  but  the  sum 
of  the  tendencies  to  unite  of  each  two  elements,  which 
sum,  he  held,  determined  the  resulting  combination  when 
several  elements  were  in  contact  with  each  other. 

7.  As  we  have  stated  in  the  History  f,  when  the  doc- 
trine of  elective  affinities  had  assumed  this  very  definite 
and  systematic  form,  it  was  assailed  by  Berthollet,  who 
maintained,  in  his  Essai  de  Statique  Chimique,  (1803,) 
that  chemical  affinities  are  not  elective :— that,  when 
various  elements  are  brought  together,  their  combinations 

*  Zymotechma,  1697,  p.  117.  t  Hist.  Ind.  Sci.,  iii.  115, 


382  PHILOSOPHY  OF  CHEMISTRY. 

do  not  depend  upon  the  kind  of  elements  alone,  but  upon 
the  quantity  of  each  which  is  present,  that  which  is 
most  abundant  always  entering  most  largely  into  the 
resulting  compounds.  It  may  seem  strange  that  it  should 
be  possible,  at  so  late  a  period  of  the  science,  to  throw 
doubt  upon  a  doctrine  which  had  presided  over  and 
directed  its  progress  so  long.  Proust  answered  Ber- 
thollet,  and  again  maintained  that  chemical  affinity  is 
elective.  I  have,  in  the  History,  given  the  judgment  of 
Berzelius  upon  this  controversy.  "  Berthollet,"  he  says, 
"  defended  himself  with  an  acuteness  which  makes  the 
reader  hesitate  in  his  judgment ;  but  the  great  mass  of 
facts  finally  decided  the  point  in  favour  of  Proust."  I 
may  here  add  the  opinion  pronounced  upon  this  subject 
by  Dr.  Turner*.  "Bergman  erred  in  supposing  the 
result  of  chemical  action  to  be  in  every  case  owing  to 
elective  affinity  [for  this  power  is  modified  in  its  effects  by 
various  circumstances]:  but  Berthollet  ran  into  the  oppo- 
site extreme  in  declaring  that  the  effects  formerly  ascribed 
to  that  power  are  never  produced  by  it.  That  chemical 
attraction  is  exerted  between  different  bodies  with  dif- 
ferent degrees  of  energy,  is,  I  apprehend,  indisputable." 
And  he  then  proceeds  to  give  many  instances  of  differ- 
ences in  affinity  which  cannot  be  accounted  for  by  the 
operation  of  any  modifying  causes.  Still  more  recently, 
M.  Dumas  has  taken  a  review  of  this  controversy ;  and, 
speaking  with  enthusiasm  of  the  work  of  Berthollet,  as 
one  which  had  been  of  inestimable  service  to  himself  in 
his  early  study  of  chemistry,  he  appears  at  first  disposed 
to  award  to  him  the  victory  in  this  dispute.  But  his 
final  verdict  leaves  undamaged  the  general  principle  now 
under  our  consideration,  that  chemical  affinity  is  elective. 
"  For  my  own  part,"  he  saysf,  "  I  willingly  admit  the  no- 

*  Chemistry,  p.  199.     6th  edition, 
t  Legons  de  Philosophic  Chimigue,  p.  386. 


IDEA  OF  CHEMICAL  AFFINITY.  883 

tions  of  Berthollet  when  we  have  to  do  with  acids  or  with 
bases,  of  which  the  energy  is  nearly  equal:  but  when 
bodies  endued  with  very  energetic  affinities  are  in  pre- 
sence of  other  bodies  of  which  the  affinities  are  very 
feeble,  I  propose  to  adopt  the  following  rule :  In  a  solu- 
tion, everything  remaining  dissolved,  the  strong  affinities 
satisfy  themselves,  leaving  the  weak  affinities  to  arrange 
matters  with  one  another.  The  strong  acids  take  the 
strong  bases,  and  the  weak  acids  can  only  unite  with  the 
weak  bases.  The  known  facts  are  perfectly  in  accordance 
with  this  practical  rule."  It  is  obvious  that  this  recog- 
nition of  a  distinction  between  strong  and  weak  affinities 
which  operates  to  such  an  extent  as  to  determine  entirely 
the  result,  is  a  complete  acknowledgement  of  the  elective 
nature  of  affinity  as  far  as  any  person  acquainted  with 
chemical  operations  could  contend  for  it.  For  it  must 
be  allowed  by  all,  that  solubility,  and  other  collateral  cir- 
cumstances, influence  the  course  of  chemical  combina- 
tions, since  they  determine  whether  or  not  there  shall 
take  place  that  contact  of  elements  without  which  affinity 
cannot  possibly  operate. 

8.  Affinity  is  Definite  as  to  Quantity. — In  proportion 
as  chemists  obtained  a  clearer  view  of  the  products  of  the 
laboratory  as  results  of  the  composition  of  elements, 
they  saw  more  and  more  clearly  that  these  results  were 
definite ;  that  one  element  not  only  preferred  to  combine 
with  another  of  a  certain  kind,  but  also  would  combine 
with  it  to  a  certain  extent  and  no  further,  thus  giving  to 
the  result  not  an  accidental  and  variable,  but  a  fixed  and 
constant  character.  Thus  salts  being  considered  as  the 
result  of  the  combination  of  two  opposite  principles,  acid 
and  alkali,  and  being  termed  neutral  when  these  prin- 
ciples exactly  balanced  each  other,  Rouelle  (who  was 
Royal  Professor  at  Paris  in  1742,)  admits  of  neutral 
salts  with  excess  of  acid,  neutral  salts  with  excess  of 


384  PHILOSOPHY    OF    CHEMISTRY. 

base,  and  perfect  neutral  salts.  Beaume  maintained* 
against  him  that  there  were  no  salts  except  those  per- 
fectly neutral,  the  other  classes  being  the  results  of  mix- 
ture and  imperfect  combination.  But  this  question  was 
not  adequately  treated  till  chemists  made  every  experi- 
ment with  the  balance  in  their  hands.  When  this  was 
done,  they  soon  discovered  that,  in  each  neutral  salt,  the 
proportional  weights  of  the  ingredients  which  composed  it 
were  always  the  same.  This  was  ascertained  by  Wenzel, 
whose  Doctrine  of  the  Affinities  of  Bodies  appeared  in 
1777.  He  not  only  ascertained  that  the  proportions  of 
elements  in  neutral  chemical  compounds  are  definite,  but 
also  that  they  are  reciprocal ;  that  is,  that  if  A,  a  certain 
weight  of  a  certain  acid,  neutralize  m,  a  certain  weight  of 
a  certain  base,  and  B,  a  certain  weight  of  a  certain  other 
acid,  neutralize  n,  a  certain  weight  of  a  certain  other  base; 
the  compound  of  A  and  n  will  also  be  neutral ;  as  also  that 
of  B  and  m.  The  same  views  were  again  presented  by 
Richter  in  1 792,  in  his  Principles  of  the  Measure  of  Che- 
mical Elements.  And  along  with  these  facts,  that  of  the 
combination  of  elements  in  multiple  proportions  being 
also  taken  into  account,  the  foundations  of  the  Atomic 
Theory  were  laid ;  and  that  theory  was  propounded  in 
1803  by  Mr.  Dalton.  That  theory,  however,  rests  upon 
the  idea  of  substance,  as  well  as  upon  that  idea  of  chemi- 
cal affinity  which  we  are  here  considering ;  and  the  dis- 
cussion of  its  evidence  and  truth  must  be  for  the  present 
deferred. 

9.  The  two  principles  just  explained,  that  affinity  is 
definite  as  to  the  kind,  and  as  to  the  quantity  of  the  ele- 
ments which  it  unites,  have  here  been  stated  as  results  of 
experimental  investigation.  That  they  could  never  have 
been  clearly  understood,  and  therefore  never  firmly  esta- 
blished, without  laborious  and  exact  experiments,  is 

*  DUMAS,  PML  Chim.,  p.  198. 


IDEA    OF   CHEMICAL    AFFINITY.  385 

certain ;  but  yet  we  may  venture  to  say  that  being  once 
known,  they  possess  an  evidence  beyond  that  of  mere 
experiment.  For  how,  in  fact,  can  we  conceive  combi- 
nations, otherwise  than  as  definite  in  kind  and  quantity? 
If  we  were  to  suppose  each  element  ready  to  combine 
with  any  other  indifferently,  and  indifferently  in  any 
quantity,  we  should  have  a  wrorld  in  which  all  would  be 
confusion  and  indefiniteness.  There  would  be  no  fixed 
kinds  of  bodies ;  salts,  and  stones,  and  ores,  would  ap- 
proach to  and  graduate  into  each  other  by  insensible  de- 
grees. Instead  of  this,  we  know  that  the  world  consists 
of  bodies  distinguishable  from  each  other  by  definite  dif- 
ferences, capable  of  being  classified  and  named,  and  of 
having  general  propositions  asserted  concerning  them. 
And  as  we  cannot  conceive  a  world  in  which  this  should 
not  be  the  case,  it  would  appear  that  we  cannot  conceive 
a  state  of  things  in  which  the  laws  of  the  combination 
of  elements  should  not  be  of  that  definite  and  measured 
kind  which  we  have  above  asserted. 

This  will,  perhaps,  appear  more  clearly  by  stating  our 
fundamental  convictions  respecting  chemical  composition 
in  another  form,  which  I  shall,  therefore,  proceed  to  do. 

10.  Chemical  Composition  determines  Physical  Proper- 
ties.— However  obscure  and  incomplete  may  be  our  con- 
ception of  the  internal  powers  by  which  the  ultimate 
particles  of  bodies  are  held  together,  it  involves,  at  least, 
this  conviction : — that  these  powers  are  what  determine 
bodies  to  be  bodies,  and  therefore  contain  the  reason  of  all 
the  properties  which,  as  bodies,  they  possess.  The  forces 
by  which  the  particles  of  a  body  are  held  together,  also 
cause  it  to  be  hard  or  soft,  heavy  or  light,  opake  or  trans- 
parent, black  or  red ;  for  if  these  forces  are  not  the 
cause  of  these  peculiarities,  what  can  be  the  cause  ?  By 
the  very  supposition  which  we  make  respecting  these 
forces,  they  include  all  the  relations  by  which  the  parts 
VOL.  i.  2  c 


386  PHILOSOPHY    OF    CHEMISTRY. 

are  combined  into  a  whole,  and  therefore  they,  and  they 
only,  must  determine  all  the  attributes  of  the  whole. 
The  foundation  of  all  our  speculations  respecting  the 
intimate  constitution  of  bodies  must  be  this,  that  their 
composition  determines  their  properties. 

Accordingly  we  find  our  chemists  reasoning  from  this 
principle  with  great  confidence,  even  in  doubtful  cases. 
Thus  Davy,  in  his  researches  concerning  the  diamond, 
says:  "That  some  chemical  difference  must  exist  between 
the  hardest  and  most  beautiful  of  the  gems  and  charcoal, 
between  a  non-conductor  and  a  conductor  of  electricity, 
it  is  scarcely  possible  to  doubt :  and  it  seems  reasonable  to 
expect  that  a  very  refined  or  perfect  chemistry  will  confirm 
the  analogies  of  nature ;  and  show  that  bodies  cannot  be 
the  same  in  their  composition  or  chemical  nature,  and 
yet  totally  different  in  their  chemical  properties."  It  is 
obvious  that  the  principle  here  assumed  is  so  far  from 
being  a  mere  result  of  experience,  that  it  is  here  appealed 
to  to  prove  that  all  previous  results  of  experience  on  this 
subject  must  be  incomplete  and  inaccurate;  and  that 
there  must  be  some  chemical  difference  between  charcoal 
and  diamond,  though  none  had  hitherto  been  detected. 

11.  In  what  manner,  according  to  what  rule,  the 
chemical  composition  shall  determine  the  kind  of  the  sub- 
stance, we  cannot  reasonably  expect  to  determine  by  mere 
conjecture  or  assumption,  without  a  studious  examination 
of  natural  bodies  and  artificial  compounds.  Yet  even  in 
the  most  recent  times,  and  among  men  of  science,  we  find 
that  an  assumption  of  the  most  arbitrary  character  has 
in  one  case  been  mixed  up  with  this  indisputable  principle, 
that  the  elementary  composition  determines  the  kind  of 
the  substance.  In  the  classification  of  minerals,  one 
school  of  mineralogists  have  rightly  taken  it  as  their  fun- 
damental principle  that  the  chemical  composition  shall 
decide  the  position  of  the  mineral  in  the  system.  But 


IDEA    OF    CHEMICAL    AFFINITY.  387 

they  have  appended  to  this  principle,  arbitrarily  and 
unjustifiably,  the  maxim  that  the  element  which  is  largest 
in  quantity  shall  fix  the  class  of  the  substance.  To  make 
such  an  assumption  is  to  renounce,  at  once,  all  hope  of 
framing  a  system  which  shall  be  governed  by  the  resem- 
blances of  the  things  classified ;  for  how  can  we  possibly 
know  beforehand  that  fifty-five  per  cent,  of  iron  shall 
give  a  substance  its  predominant  properties,  and  that 
forty-five  per  cent,  shall  not  ?  Accordingly,  the  systems 
of  mineralogical  arrangement  which  have  been  attempted 
in  this  way,  (those  of  Haiiy,  Phillips,  and  others,)  have 
been  found  inconsistent  with  themselves,  ambiguous,  and 
incapable  of  leading  to  any  general  truths. 

12.  Thus  the  physical  properties  of  bodies  depend 
upon  their  chemical  composition,  but  in  a  manner  which 
a  general  examination  of  bodies  with  reference  to  their 
properties  and  their  composition  can  alone  determine. 
We  may,  however,  venture  to  assert  further,  that  the 
more  definite  the  properties  are,  the  more  distinct  may 
we  expect  to  find  this  dependence.  Now  the  most 
definite  of  the  properties  of  bodies  are  those  constant 
properties  which  involve  relations  of  space :  that  is,  their 
figure.  We  speak  not,  however,  of  that  external  figure, 
derived  from  external  circumstances,  which,  so  far  from 
being  constant  and  definite,  is  altogether  casual  and  arbi- 
trary; but  of  that  figure  which  arises  from  their  internal 
texture,  and  which  shows  itself  not  only  in  the  regular 
forms  which  they  spontaneously  assume,  but  in  the 
disposition  of  the  parts  to  separate  in  definite  directions 
and  no  others.  In  short,  the  most  definite  of  the  pro- 
perties of  perfect  chemical  compounds  is  their  crystalline 
structure ;  and  therefore  it  is  evident  that  the  crystalline 
structure  of  each  body,  and  the  forms  which  it  affects, 
must  be  in  a  most  intimate  dependence  upon  its  chemical 
composition. 

2  c  2 


388  PHILOSOPHY  OF  CHEMISTRY. 

Here  again  we  are  led  to  the  brink  of  another  theory; 
— that  of  crystalline  structure,  which  has  excited  great 
interest  among  philosophers  ever  since  the  time  of 
Haiiy.  But  this  theory  involves,  besides  that  idea  of 
chemical  composition  with  which  we  are  here  concerned, 
other  conceptions  which  enter  into  the  relations  of 
figure.  These  conceptions,  governed  principally  by  the 
idea  of  Symmetry,  must  be  unfolded  and  examined  before 
we  can  venture  to  discuss  any  theory  of  crystallization : 
and  we  shall  proceed  to  do  this  as  soon  as  we  have 
first  duly  considered  the  Idea  of  Substance  and  its  con- 
sequences. 


CHAPTER  III. 
OF  THE  IDEA  OF  SUBSTANCE. 

1.  Axiom  of  the  Indestructibility  of  Substance. — We 
now  come  to  an  Idea  of  which  the  history  is  very  different 
from  those  of  which  we  have  lately  been  speaking. 
Instead  of  being  gradually  and  recently  brought  into  a 
clear  light,  as  has  been  the  case  with  the  Ideas  of  Polarity 
and  Affinity,  the  Idea  of  Substance  has  been  entertained 
in  a  distinct  form  from  the  first  periods  of  European 
speculation.  That  this  is  so,  is  proved  by  our  finding  a 
principle  depending  upon  this  idea  current  as  an  axiom 
among  the  early  philosophers  of  Greece : — namely,  that 
nothing  can  be  produced  out  of  nothing.  Such  an  axiom, 
more  fully  stated,  amounts  to  this :  that  the  substance  of 
which  a  body  consists  is  incapable  of  being  diminished 
(and  consequently  incapable  of  being  augmented)  in 
quantity,  whatever  apparent  changes  it  may  undergo. 
Its  form,  its  distribution,  its  qualities  may  vary,  but  the 
substance  itself  is  identically  the  same  under  all  these 
variations. 


IDEA    OF    SUBSTANCE.  389 

The  axiom  just  spoken  of  was  the  great  principle  of 
the  physical  philosophy  of  the  Epicurean  school,  as  it 
must  be  of  every  merely  material  philosophy.  The 
reader  of  Lucretius  will  recollect  the  emphasis  with 
which  it  is  repeatedly  asserted  in  his  poem : 

E  nilo  nil  gigni,  in  niluin  nil  posse  reverti ; 
Nought  comes  of  nought,  nor  ought  returns  to  nought. 

Those  who  engaged  in  these  early  attempts  at  physical 
speculation  were  naturally  much  pleased  with  the  clear- 
ness which  was  given  to  their  notions  of  change,  compo- 
sition, and  decomposition,  by  keeping  steadily  hold  of  the 
Idea  of  Substance,  as  marked  by  this  fundamental  axiom. 
Nor  has  its  authority  ever  ceased  to  be  acknowledged. 
A  philosopher  was  asked  *,  What  is  the  weight  of  smoke  ? 
He  answered,  Subtract  the  weight  of  the  ashes  from  the 
weight  of  the  wood  which  is  burnt,  and  you  have  the 
weight  of  the  smoke.  This  reply  would  be  assented  to 
by  all ;  and  it  assumes  as  incontestable  that  even  under 
the  action  of  fire,  the  material,  the  substance,  does  not 
perish,  but  only  changes  its  form. 

This  principle  of  the  indestructibility  of  substance 
might  easily  be  traced  in  many  reasonings  and  researches, 
ancient  and  modern.  For  instance,  when  the  chemist 
works  with  the  retort,  he  places  the  body  on  which  he 
operates  in  one  part  of  an  inclosed  cavity,  which,  by  its 
bendings  and  communications,  separates  at  the  same 
time  that  it  confines,  the  products  which  result  from 
the  action  of  fire :  and  he  assumes  that  this  process 
is  an  analysis  of  the  body  into  its  ingredients,  not  a 
creation  of  anything  which  did  not  exist  before,  or  a 
destruction  of  anything  which  previously  existed.  And 
he  assumes  further,  that  the  total  quantity  of  the  sub- 
stance thus  analysed  is  the  sum  of  the  quantities  of  its 
ingredients.  This  principle  is  the  very  basis  of  chemical 
speculation  as  we  shall  hereafter  explain  more  fully. 
*  KANT,  Kritik,  <kr  R.  F.,  p.  16?. 


390  PHILOSOPHY  OF  CHEMISTRY. 

2.  The  Idea  of  Substance. — The  axiom  above  spoken 
of  depends  upon  the  Idea  of  Substance,  which  is  involved 
in  all  our  views  of  external  objects.  We  unavoidably 
assume  that  the  qualities  and  properties  which  we  observe 
are  properties  of  things; — that  the  adjective  implies  a 
substantive ; — that  there  is,  besides  the  external  characters 
of  things,  something  of  which  they  are  the  characters. 
An  apple  which  is  red,  and  round,  and  hard,  is  not  merely 
redness,  and  roundness,  and  hardness :  these  circum- 
stances may  all  alter  while  the  apple  remains  the  same 
apple.  Behind  the  appearances  which  we  see,  we  con- 
ceive something  of  which  we  think ;  or  to  use  the 
metaphor  which  obtained  currency  among  the  ancient 
philosophers,  the  attributes  and  qualities  which  we  observe 
are  supported  by  and  inherent  in  something :  and  this 
something  is  hence  called  a  substratum  or  substance,  that 
which  stands  beneath  the  apparent  qualities  and  supports 
them. 

That  we  have  such  an  Idea,  using  the  term  in  the 
sense  in  which  I  have  employed  it  throughout  these 
disquisitions,  is  evident  from  what  has  been  already  said. 
The  Axiom  of  the  indestructibility  of  substance  proves 
the  existence  of  the  Idea  of  Substance,  just  as  the  Axioms 
of  Geometry  and  Arithmetic  prove  the  existence  of  the 
Ideas  of  Space  and  Number.  In  the  case  of  substance, 
as  of  space  or  number,  the  ideas  cannot  be  said  to  be 
borrowed  from  experience,  for  the  axioms  have  an 
authority  of  a  far  more  comprehensive  and  demonstrative 
character  than  any  which  experience  can  bestow.  The 
axiom  that  nothing  can  be  produced  from  nothing  and 
nothing  destroyed,  is  so  far  from  being  a  result  of  expe- 
rience, that  it  is  apparently  contradicted  by  the  most 
obvious  observation.  It  has,  at  first,  the  air  of  a  paradox, 
and  by  those  who  refer  to  it,  it  is  familiarly  employed  to 
show  how  fallacious  common  observation  is.  The  asser- 


IDEA  OF  SUBSTANCE.  391 

tion  is  usually  made  in  this  form ;  that  nothing  is  created 
and  nothing  annihilated,  notwithstanding  that  the  common 
course  of  our  experience  appears  to  show  the  contrary. 
The  principle  is  not  an  empirical,  but  a  necessary  and 
universal  truth :  is  collected,  not  from  the  evidence  of 
our  senses,  but  from  the  operation  of  our  ideas.  And 
thus  the  universal  and  undisputed  authority  of  the  axiom 
proves  the  existence  of  the  Idea  of  Substance. 

3.  Lockers  Denial  of  the  Idea  of  Substance. — I  shall 
not  attempt  to  review  the  various  opinions  which  have 
been  promulgated  respecting  this  idea :  but  it  may  be 
worth  our  while  to  notice  briefly  the  part  it  played  in 
the  great  controversy  concerning  the  origin  of  our  ideas 
which  LOCKE'S  Essay  occasioned.  Locke's  object  was  to 
disprove  the  existence  of  all  ideas  not  derived  from 
Sensation  or  Reflection :  and  since  the  idea  of  substance 
as  distinct  from  external  qualities,  is  manifestly  not  derived 
directly  from  sensation,  nor  by  any  very  obvious  or  dis- 
tinct process  from  reflection,  Locke  was  disposed  to 
exclude  the  idea  as  much  as  possible.  Accordingly,  in 
his  argumentation  against  Innate  Ideas  *,  he  says  plainly, 
"  the  idea  of  substance,  which  we  neither  have  nor  can. 
have  by  sensation  or  reflection."  And"  the  inference 
which  he  draws  is,  "  that  we  have  no  such  clear  idea  at 
all."  What  then,  it  may  be  asked,  do  we  mean  by  the 
word  substance?  This  also  he  answers,  though  some- 
what strangely,  "We  signify  nothing  by  the  word 
substance,  but  only  an  uncertain  supposition  of  we  know 
not  what,  i.  e.9  of  something  whereof  we  have  no  par- 
ticular distinct  positive  idea,  which  we  take  to  be  the 
substratum,  or  support,  of  those  ideas  we  know."  That 
while  he  indulged  in  this  tautological  assertion  of  our 
ignorance  and  uncertainty,  he  should  still  have  been 
compelled  to  acknowledge  that  the  word  substance  had 

*  Essay,  b,  i.,  ch.  4,?  s.  18. 


302  PHILOSOPHY  OF  CHEMISTRY. 

some  meaning,  and  should  have  been  driven  to  explain  it 
by  the  identical  metaphors  of  substratum  and  support,  is 
a  curious  proof  how  impossible  it  is  entirely  to  reject  this 
idea. 

But  as  we  have  already  seen,  the  supposition  of  the 
existence  of  substance  is  so  far  from  being  uncertain,  that 
it  carries  with  it  irresistible  conviction,  and  substance  is 
necessarily  conceived  as  something  which  cannot  be  pro- 
duced or  destroyed.  It  may  be  easily  supposed,  therefore, 
that  when  the  controversy  between  Locke  and  his  assail- 
ants came  to  this  point,  he  would  be  in  some  difficulty. 
And,  indeed,  though  with  his  accustomed  skill  in  contro- 
versy, he  managed  to  retain  a  triumphant  tone,  he  was 
driven  from  his  main  points.  Thus  he  repels  the  charge 
that  he  took  the  being  of  substance  to  be  doubtful*. 
He  says,  "  Having  everywhere  affirmed  and  built  upon  it 
that  man  is  a  substance,  I  cannot  be  supposed  to  question 
or  doubt  of  the  being  of  substance,  till  I  can  question  or 
doubt  of  my  own  being."  He  attempts  to  make  a  stand 
by  saying  that  being  of  things  does  not  depend  upon  our 
ideas ;  but  if  he  had  been  asked  how,  without  having  an 
idea  of  substance,  he  knew  substance  to  be,  it  is  difficult 
to  conceive  what  answer  he  could  have  made.  Again,  he 
had  said  that  our  idea  of  substance  arises  from  our 
accustoming  ourselves  to  suppose  a  substratum  of  qua- 
lities. Upon  this  his  adversary,  Bishop  Stillingfleet,  very 
properly  asks,  Is  this  custom  grounded  upon  true  reason 
or  no  ?  To  which  Locke  replies,  that  it  is  grounded  upon 
this :  That  we  cannot  conceive  how  simple  ideas  of  sensible 
qualities  should  subsist  alone ;  and  therefore  we  suppose 
them  to  exist  in,  and  to  be  supported  by  some  common 
subject,  which  support  we  denote  by  the  name  substance. 
Thus  he  allows,  not  only  that  we  necessarily  assume  the 
reality  of  substance,  but  that  we  cannot  conceive  qualities 
*  Essay,  b.  ii.,  ch.  2,  and  First  Letter  to  the  Bishop  of  Worcester. 


IDEA  OF  SUBSTANCE.  393 

without  substance ;  which  are  concessions  so  ample  as 
almost  to  include  all  that  any  advocate  for  the  Idea  of 
Substance  need  desire. 

Perhaps  Locke,  and  the  adherents  of  Locke,  in  deny- 
ing that  we  have  an  idea  of  substance  in  general,  were 
latently  influenced  by  finding  that  they  could  not,  by  any 
effort  of  mind,  call  up  any  image  winch  could  be  con- 
sidered as  an  image  of  substance  in  general.  That  in 
this  sense  we  have  no  idea  of  substance,  is  plain  enough ; 
but  in  the  same  sense  we  have  no  idea  of  space  in 
general,  or  of  time,  or  number,  or  cause,  or  resemblance. 
Yet  we  certainly  have  such  a  power  of  representing  to 
our  minds  space,  time,  number,  cause,  resemblance,  as  to 
arrive  at  numerous  truths  by  means  of  such  representa- 
tions. These  general  representations  I  have  all  along- 
called  Ideas,  nor  can  I  discover  any  more  appropriate 
word ;  and  in  this  sense,  we  have  also,  as  has  now  been 
shown,  an  Idea  of  Substance. 

4.  Is  all  Material  Substance  heavy? — The  principle 
that  the  quantity  of  the  substance  of  any  body  remains 
unchanged  by  our  operations  upon  it,  is,  as  we  have  said, 
of  universal  validity.  But  then  the  question  occurs,  how 
are  we  to  ascertain  the  quantity  of  substance,  and  thus 
to  apply  the  principle  in  particular  cases.  In  the  case 
above  mentioned,  where  smoke  was  to  be  weighed,  it 
was  manifestly  assumed  that  the  quantity  of  the  substance 
might  be  known  by  its  weight ;  and  that  the  total 
quantity  being  unchanged,  the  total  weight  also  would 
remain  the  same.  Now  on  what  grounds  do  we  make 
this  assumption  ?  Is  all  material  substance  heavy  ?  and 
if  we  can  assert  this  to  be  so,  on  what  grounds  does  the 
truth  of  the  assertion  rest  ?  These  are  not  idle  questions 
of  barren  curiosity ;  for  in  the  history  of  that  science 
(Chemistry)  to  which  the  idea  of  substance  is  principally 
applicable,  nothing  less  than  the  fate  of  a  comprehensive 


394  PHILOSOPHY  OF  CHEMISTRY. 

and  long  established  theory  (the  Phlogiston  theory) 
depended  upon  the  decision  of  this  question.  When  it 
.was  urged  that  the  reduction  of  a  metal  from  a  calcined 
to  a  metallic  form  could  not  consist  in  the  addition  of 
phlogiston,  because  the  metal  was  lighter  than  the  calx 
had  been ;  it  was  replied  by  some,  that  this  was  not  con- 
clusive, for  that  phlogiston  was  a  principle  of  levity, 
diminishing  the  weight  of  the  body  to  which  it  was 
added.  This  reply  was,  however,  rejected  by  all  the 
sounder  philosophers,  and  the  force  of  the  argument 
finally  acknowledged.  But  why  was  this  suggestion  of  a 
substance  having  no  weight,  or  having  absolute  levity, 
repudiated  by  the  most  reflective  reasoners?  It  is  as- 
sumed, it  appears,  that  all  matter  must  be  heavy;  what  is 
the  ground  of  this  assumption  ? 

The  ground  of  such  an  assumption  appears  to  be  the 
following.  Our  idea  of  substance  includes  in  it  this : 
that  substance  is  a  quantity  capable  of  addition ;  and 
thus  capable  of  making  up,  by  composition,  a  sum  equal 
to  all  its  parts.  But  substance,  and  the  quantity  of  sub- 
stance, can  be  known  to  us  only  by  its  attributes  and  qua- 
lities. And  the  qualities  which  are  capable  constantly 
and  indefinitely  of  increase  and  diminution  by  increase 
and  diminution  of  the  parts,  must  be  conceived  insepa- 
rable from  the  substance.  For  the  qualities,  if  removable 
from  the  substance  at  all,  must  be  removable  by  some 
operation  performed  upon  the  substance;  and  by  the 
idea  of  substance,  all  such  operations  are  only  equivalent 
to  separation,  junction,  and  union  of  parts.  Hence  those 
characters  which  thus  universally  increase  and  diminish 
by  addition  and  subtraction  of  the  things  themselves, 
belong  to  the  substance  of  the  things.  They  are  measures 
of  quantity,  and  not  merely  separable  qualities. 

The  weight  of  bodies  is  such  a  character.  However 
we  compound  or  divide  bodies,  we  compound  and  divide 


IDEA   OF    SUBSTANCE.  895 

their  weight  in  the  same  manner.  We  may  dismember  a 
body  into  the  minutest  parts ;  but  the  sum  of  the  weights 
of  the  parts  is  always  equal  to  the  whole  weight  of  the 
body.  The  weight  of  a  body  can  be  in  no  way  increased 
or  diminished  except  by  adding  something  to  it  or  taking- 
something  from  it.  If  we  bake  a  brick,  we  do  not  con- 
ceive that  the  change  of  colour  or  of  hardness,  implies 
that  anything  has  been  created  or  destroyed.  It  may 
easily  be  that  the  parts  have  only  assumed  a  new 
arrangement ;  but  if  the  brick  have  lost  weight,  we  sup- 
pose that  something  (moisture  for  instance,)  has  been 
removed  elsewhere. 

Thus  weight  is  apprehended  as  essential  to  matter. 
In  considering  the  dismemberment  or  analysis  of  bodies, 
we  assume  that  there  must  be  some  criterion  of  the  quan- 
tity of  substance  ;  and  this  criterion  can  possess  no  other 
properties  than  their  weight  possesses.  If  we  assume 
an  element  which  has  no  weight,  or  the  weight  of 
which  is  negative,  as  some  of  the  defenders  of  phlo- 
giston attempted  to  do,  we  put  an  end  to  all  speculation 
on  such  subjects.  For  if  weight  is  not  the  criterion  of 
the  quantity  of  one  element,  phlogiston  for  instance,  why 
is  weight  the  criterion  of  the  quantity  of  any  other  ele- 
ment ?  We  may,  by  the  same  right,  assume  any  other 
real  or  imaginary  element  to  have  levity  instead  of  gra- 
vity ;  or  to  have  a  peculiar  intensity  of  gravity  which 
makes  its  weight  no  index  of  its  quantity.  In  short,  if 
we  do  this,  we  deprive  of  all  possibility  of  application  our 
notions  of  element,  analysis,  and  composition ;  and  vio- 
late the  postulates  on  which  the  questions  are  propounded 
which  we  thus  attempt  to  decide. 

We  must,  then,  take  a  constant  and  quantitative  pro- 
perty of  matter,  such  as  weight  is,  to  be  an  index  of  the 
quantity  of  matter  or  of  substance  to  which  it  belongs. 
I  do  not  here  speak  of  the  question  which  has  sometimes 


396  PHILOSOPHY   OF   CHEMISTRY. 

been  proposed,  whether  the  iveight  or  the  inertia  of 
bodies  be  the  more  proper  measure  of  the  quantity  of 
matter.  For  the  measure  of  inertia  is  regulated  by  the 
same  assumption  as  that  of  substance : — that  the  quantity 
of  the  whole  must  be  equal  to  the  quantity  of  all  the 
parts :  and  inertia  is  measured  by  weight,  for  the  same 
reason  that  substance  is  so. 

Having  thus  established  the  certainty,  and  ascertained 
the  interpretation  of  the  fundamental  principle  which  the 
Idea  of  Substance  involves,  we  are  prepared  to  consider 
its  application  in  the  science  upon  which  it  has  a  peculiar 
bearing. 


CHAPTER  IV. 

APPLICATION   OF   THE   IDEA  OF  SUBSTANCE  IN 
CHEMISTRY. 

1.  A  Body  is  Equal  to  the  Sum  of  its  Elements. — 
From  the  earliest  periods  of  chemistry  the  balance  has 
been  familiarly  used  to  determine  the  proportions  of  the 
ingredients  and  of  the  compound ;  and  soon  after  the 
middle  of  the  last  century,  this  practice  was  so  studiously 
followed,  that  Wenzel  and  Richter  were  thereby  led  to 
the  doctrine  of  definite  proportions.  But  yet  the  full 
value  and  significance  of  the  balance,  as  an  indispensable 
instrument  in  chemical  researches,  was  not  understood  till 
the  gaseous,  as  well  as  solid  and  fluid  ingredients  were 
taken  into  the  account.  When  this  was  done,  it  was 
found  that  the  principle,  that  the  whole  is  equal  to  the 
sum  of  its  parts,  of  which,  as  we  have  seen,  the  necessary 
truth,  in  such  cases,  flows  from  the  idea  of  substance, 
could  be  applied  in  the  most  rigorous  manner.  And  con- 
versely, it  was  found  that  by  the  use  of  the  balance,  the 
chemist  could  decide,  in  doubtful  cases,  which  was  a 
whole,  and  which  were  parts. 


APPLICATION  OF  THE  IDEA  OF  SUBSTANCE.  397 

For  it  may  be  observed  that  chemistry  considers  all 
the  changes  which  belong  to  her  province  as  compositions 
and  decompositions  of  elements :  but  still  the  question 
may  occur,  whether  an  observed  change  be  the  one  or 
the  other.  How  can  we  distinguish  whether  the  process 
which  we  contemplate  be  composition  or  decomposition? 
Whether  the  new  body  be  formed  by  addition  of  a  new, 
or  subtraction  of  an  old  element  ?  Again  ;  in  the  case  of 
decomposition,  we  may  inquire,  what  are  the  ultimate 
limits  of  our  analysis  ?  If  we  decompound  bodies  into 
others  more  and  more  simple,  how  far  can  we  carry  this 
succession  of  processes  ?  How  far  can  we  proceed  in  the 
road  of  analysis  ?  And  in  our  actual  course,  what  evidence 
have  we  that  our  progress,  as  far  as  it  has  gone,  has  carried 
us  from  the  more  complex  to  the  more  simple?  To  this  we 
reply,  that  the  criterion  which  enables  us  to  distinguish, 
decidedly  and  finally,  whether  our  process  have  been  a 
mere  analysis  of  the  proposed  body  into  its  ingredients,  or 
a  synthesis  of  some  of  them  with  some  new  element,  is 
the  principle  stated  above,  that  the  weight  of  the  whole  is 
equal  to  the  weight  of  all  the  parts.  And  no  process  of 
chemical  analysis  or  synthesis  can  be  considered  complete 
till  it  has  been^ verified  by  this  fact ; — by  finding  that  the 
weight  of  the  compound  is  the  weight  of  its  supposed  in- 
gredients ;  or,  that  if  there  be  an  element  which  we  think 
we  have  detached  from  the  whole,  its  loss  is  betrayed  by  a 
corresponding  diminution  of  weight. 

I  have  already  noticed  what  an  important  part  this 
principle  has  played  in  the  great  chemical  controversy 
which  ended  in  the  establishment  of  the  oxygen  theory, 
The  calcination  of  a  metal  was  decided  to  be  the  union 
of  oxygen  with  the  metal,  and  not  the  separation  of 
phlogiston  from  it,  because  it  was  found  that  in  the  pro- 
cess of  calcination,  the  weight  of  the  metal  increased, 
and  increased  exactly  as  much  as  the  weight  of  ambient 


398  PHILOSOPHY   OF   CHEMISTRY. 

air  diminished.  When  oxygen  and  hydrogen  were  ex- 
ploded together,  and  a  small  quantity  of  water  was  pro- 
duced, it  was  held  that  this  was  really  a  synthesis  of 
water,  because,  when  very  great  care  was  taken  with  the 
process,  the  weight  of  the  water  which  resulted  was  equal 
to  the  weight  of  the  gases  which  disappeared. 

2.  Lavoisier. — It  was  when  gases  came  to  be  con- 
sidered as  entering  largely  into  the  composition  of  liquid 
and  solid  bodies,  that  extreme  accuracy  in  weighing  was 
seen  to  be  so  necessary  to  the  true  understanding  of 
chemical  processes.  It  was  in  this  manner  discovered  by 
Lavoisier  and  his  contemporaries  that  oxygen  constitutes 
a  large  ingredient  of  calcined  metals,  of  acids,  and  of 
water.  A  countryman  of  Lavoisier*  has  not  only  given 
most  just  praise  to  that  great  philosopher  for  having  con- 
stantly tested  all  his  processes  by  a  careful  and  skilful  use 
of  the  balance,  but  has  also  claimed  for  him  the  merit  of 
having  introduced  the  maxim,  that  in  chemical  operations 
nothing  is  created  and  nothing  lost.  But  I  think  it  is 
impossible  to  deny  that  this  maxim  is  assumed  in  all  the 
attempts  at  analysis  made  by  his  contemporaries,  as  well 
as  by  him.  This  maxim  is  indeed  included  in  any  clear 
notion  of  analysis:  it  could  not  be  the  result  of  the 
researches  of  any  one  chemist,  but  was  the  governing 
principle  of  the  reasonings  of  all.  Lavoisier,  however, 
employed  this  principle  with  peculiar  assiduity  and  skill. 
In  applying  it,  he  does  not  confine  himself  to  mere  addi- 
tions and  subtractions  of  the  quantities  of  ingredients ; 
but  often  obtains  his  results  by  more  complex  processes. 
In  one  of  his  investigations  he  says,  "  I  may  consider  the 
ingredients  which  are  brought  together,  and  the  result 
which  is  obtained  as  an  algebraical  equation ;  and  if  I 
successively  suppose  each  of  the  quantities  of  this  equation 
to  be  unknown,  I  can  obtain  its  value  from  the  rest :  and 

*  M.  DUMAS,  Leqonsch  la  Philosophic  Chimiqw.    1837.  p.  157. 


APPLICATION  OF  THE  IDEA  OF  SUBSTANCE.  399 

thus  I  can  rectify  the  experiment  by  the  calculation,  and 
the  calculation  by  the  experiment.  I  have  often  taken 
advantage  of  this  method,  in  order  to  correct  the  first 
results  of  my  experiments,  and  to  direct  me  in  repeating 
them  with  proper  precautions." 

The  maxim  that  the  whole  is  equal  to  the  sum  of  all 
its  parts,  is  thus  capable  of  most  important  and  varied 
employment  in  chemistry.  But  it  may  be  applied  in 
another  form  to  the  exclusion  of  a  class  of  speculations 
which  are  often  put  forwards. 

3.  Maxim  respecting  Imponderable  Elements. — Several 
of  the  phenomena  which  belong  to  bodies,  as  heat,  light, 
electricity,  magnetism,  have  been  explained  hypothetical ly 
by  assuming  the  existence  of  certain  fluids;  but  these  fluids 
have  never  been  shown  to  have  weight.  Hence  such 
hypothetical  fluids  have  been  termed  imponderable  elements. 
It  is  however  plain,  that  so  long  as  these  fluids  appear 
to  be  without  weight,  they  are  not  elements  of  bodies  in 
the  same  sense  as  those  elements  of  which  we  have 
hitherto  been  speaking.  Indeed  we  may  with  good 
reason  doubt  whether  those  phenomena  depend  upon 
transferable  fluids  at  all.  We  have  seen  strong  reason 
to  believe  that  light  is  not  matter,  but  only  motion ;  and 
the  same  thing  appears  to  be  probable  with  regard  to 
heat.  Nor  is  it  at  all  inconceivable  that  a  similar  hypo- 
thesis respecting  electricity  and  magnetism  should  here- 
after be  found  tenable.  Now  if  heat,  light,  and  those 
other  agents,  be  not  matter,  they  are  not  elements  in 
such  a  sense  as  to  be  included  in  the  principle  referred 
to  above,  that  the  body  is  equal  to  the  sum  of  its  ele- 
ments. Consequently  the  maxim  just  stated,  that  in 
chemical  operations  nothing  is  created,  nothing  annihi- 
lated, does  not  apply  to  light  and  heat.  They  are  not 
things.  And  whether  heat  can  be  produced  where  there 
was  no  heat  before,  and  light  struck  out  from  darkness, 


400  PHILOSOPHY  OF   CHEMISTRY. 

the  ideas  of  which  we  are  at  present  treating  do  not 
enable  us  to  say.  In  reasoning  respecting  chemical 
synthesis  and  analysis  therefore,  we  shall  only  make  con- 
fusion by  attempting  to  include  in  our  conception  the 
light  and  heat  which  are  produced  and  destroyed.  Such 
phenomena  may  be  very  proper  subjects  of  study,  as 
indeed  they  undoubtedly  are  ;  but  they  cannot  be  studied 
to  advantage  by  considering  them  as  sharing  the  nature 
of  composition  and  decomposition. 

Again :  in  all  attempts  to  explain  the  processes  of 
nature,  the  proper  course  is,  first  to  measure  the  facts 
with  precision,  and  then  to  endeavour  to  understand 
their  cause.  Now  the  facts  of  chemical  composition  and 
decomposition,  the  weights  of  the  ingredients  and  of  the 
compounds,  are  facts  measurable  with  the  utmost  preci- 
sion and  certainty.  But  it  is  far  otherwise  with  the  light 
and  heat  which  accompany  chemical  processes.  When 
combustion,  deflagration,  explosion,  takes  place,  how  can 
we  measure  the  light  or  the  heat?  Even  in  cases  of 
more  tranquil  action,  though  we  can  apply  the  thermo- 
meter, what  does  the  thermometer  tell  us  respecting  the 
quantity  of  the  heat  ?  Since  then  we  have  no  measure 
which  is  of  any  value  as  regards  such  circumstances  in 
chemical  changes,  if  we  attempt  to  account  for  these 
phenomena  on  chemical  principles,  we  introduce,  into 
investigations  in  themselves  perfectly  precise  and  mathe- 
matically rigorous,  another  class  of  reasonings,  vague 
and  insecure,  of  which  the  only  possible  effect  is  to  vitiate 
the  whole  reasoning,  and  to  make  our  conclusions  ine- 
vitably erroneous. 

We  are  led  then  to  this  maxim  :  that  imponderable 
fluids  are  not  to  be  admitted  as  chemical  elements  of  bodies*. 

*  Since  we  are  thus  warned  by  a  sound  view  of  the  nature  of 
science,  from  considering  chemical  affinity  as  having  any  hold  upon 
imponderable  elements,  we  are  manifestly  still  more  decisively  pro- 


APPLICATION  OF  THE  IDEA  OF  SUBSTANCE.  401 

4.  It  appears,  I  think,  that  our  best  and  most  philo- 
sophical chemists  have  proceeded  upon  this  principle  in 
their  investigations.  In  reasoning  concerning  the  consti- 
tution of  bodies  and  the  interpretation  of  chemical  changes, 
the  attempts  to  include  in  these  interpretations  the  heat 
or  cold  produced,  by  the  addition  or  subtraction  of  a 
certain  hypothetical  caloric,  have  become  more  and  more 
rare  among  men  of  science.  Such  statements,  and  the 
explanations  often  put  forwards  of  the  light  and  heat 
which  appear  under  various  circumstances  in  the  form  of 
fire,  must  be  considered  as  unessential  parts  of  any  sound 
theory.  Accordingly  we  find  Mr.  Faraday  gradually 
relinquishing  such  views.  In  January,  1834,  he  speaks 
generally  of  an  hypothesis  of  this  kind*.  "I  cannot 
refrain  from  recalling  here  the  beautiful  idea  put  forth, 
I  believe  by  Berzelius,  in  his  developement  of  his  views 
of  the  electro-chemical  theory  of  affinity,  that  the  heat 
and  light  evolved  during  cases  of  powerful  combination 
are  the  consequence  of  the  electric  discharge  which  is  at 
that  moment  taking  place."  But  in  April  of  the  same 
yearf,  he  observes,  that  in  the  combination  of  oxygen 
and  hydrogen  to  produce  water,  electric  powers  to  a  most 
enormous  amount  are  for  the  time  active,  but  that  the 
flame  which  is  produced  gives  but  feeble  traces  of  such 
powers.  "  Such  phenomena,"  therefore,  he  adds,  "  may 
not,  cannot  be,  taken  as  evidences  of  the  nature  of  the 
action ;  but  are  merely  incidental  results,  incomparably 
small  in  relation  to  the  forces  concerned,  and  supplying 
no  information  of  the  way  in  which  the  particles  are 

hibited  from  supposing  mechanical  impulse  or  pressure  to  have  any 
effect  upon  such  elements.  To  make  this  supposition,  is  to  connect 
the  most  subtle  and  incorporeal  objects  which  we  know  in  nature  by 
the  most  material  ties.  This  remark  seems  to  be  applicable  to  M. 
Poisson's  hypothesis  that  the  electric  fluid  is  retained  at  the  surface  .of 
bodies  by  the  pressure  of  the  atmosphere. 

*  Researches,  870,  t  Ib.  960. 

VOL.   I.  2  D 


402  PHILOSOPHY    OF    CHEMISTRY. 

active  on  each  other,  or  in  which  their  forces  are  finally 
arranged." 

In  pursuance  of  this  maxim,  we  must  consider  as 
unessential  parts  of  the  oxygen  theory  that  portion  of  it, 
much  insisted  upon  by  its  author  at  the  time,  in  which 
when  sulphur,  for  instance,  combined  with  oxygen  to 
produce  sulphuric  acid,  the  combustion  was  accounted 
for  by  means  of  the  caloric  which  was  supposed  to  bo 
liberated  from  its  combination  with  oxygen. 

5.  Controversy  of  the  Composition  of  Water. — There 
is  another  controversy  of  our  times  to  which  we  may 
witli  great  propriety  apply  the  maxim  now  before  us. 
After  the  glory  of  having  first  given  a  true  view  of  the 
composition  of  water  had  long  rested  tranquilly  upon 
the  names  of  Cavendish  and  Lavoisier,  a  claim  was 
made  in  favour  of  James  Watt  as  the  real  author  of  this 
discovery  by  his  son,  (Mr.  J.  Watt,)  and  his  eulogist, 
(M.  Arago*.)  It  is  not  to  our  purpose  here  to  discuss 
the  various  questions  which  have  arisen  on  this  subject 
respecting  priority  of  publication,  and  respecting  the 
translation  of  opinions  published  at  one  time  into  the 
language  of  another  period.  But  if  we  look  at  Watt's 
own  statement  of  his  views,  given  soon  after  those  of 
Cavendish  had  been  published,  we  shall  perceive  that 
it  is  marked  by  a  violation  of  this  maxim:  we  shall 
find  that  he  does  admit  imponderable  fluids  as  chemical 
elements;  and  thus  shows  a  great  vagueness  and 
confusion  in  his  idea  of  chemical  composition.  With 
such  imperfection  in  his  views,  it  is  not  surprising  that 
Watt,  not  only  did  not  anticipate,  but  did  not  fully 
appreciate  the  discovery  of  Cavendish  and  Lavoisier. 
Watt's  statement  of  his  views  is  as  followsf: — "Are  we 
not  authorized  to  conclude  that  water  is  composed  of 

*  Eloge  cle  James  Watt,  Annuaire  du  Bur.  clcs  Long.^  1839. 
t  Phil  Trans.,  1784,  p.  332. 


APPLICATION    OP  THE  IDEA  OF  SUBSTANCE.  403 

dephlogisticated  air  and  phlogiston  deprived  of  part  of 
their  latent  or  elementary  heat ;  that  dephlogisticated  or 
pure  air  is  composed  of  water  deprived  of  its  phlogiston 
and  united  to  elementary  heat  and  light ;  and  that  the 
latter  are  contained  in  it  in  a  latent  state,  so  as  not  to 
be  sensible  to  the  thermometer  or  to  the  eye ;  and  if 
light  be  only  a  modification  of  heat,  or  a  circumstance 
attending  it,  or  a  component  part  of  the  inflammable  air, 
then  pure  or  dephlogisticated  air  is  composed  of  water 
deprived  of  its  phlogiston  and  united  to  elementary  heat  ?" 

When  we  compare  this  doubtful  and  hypothetical 
statement,  involving  so  much  that  is  extraneous  and  hete- 
rogeneous, with  the  conclusion  of  Cavendish,  in  which 
there  is  nothing  hypothetical  or  superfluous,  we  may  con- 
fidently assent  to  the  decision  which  has  been  pronounced 
by  one*  of  our  own  time  in  favour  of  Cavendish.  And 
we  may  with  pleasure  recognise,  in  this  enlightened  um- 
pire, a  due  appreciation  of  the  value  of  the  maxim  on 
which  we  are  now  insisting.  "Cavendish,"  says  Mr. 
Vernon  Harcourt,  "pared  off  from  the  hypotheses  their 
theories  of  combustion,  and  affinities  of  imponderable  for 
ponderable  matter,  as  complicating  chemical  with  physical 
considerations." 

6.  Relation  of  Heat  to  Chemistry. — But  while  we 
thus  condemn  the  attempts  to  explain  the  thermotical 
phenomena  of  chemical  processes  by  means  of  che- 
mical considerations,  it  may  be  asked  if  we  are  alto- 
gether to  renounce  the  hope  of  understanding  such 
phenomena?  It  is  plain,  it  may  be  said,  that  heat  gene- 
rated in  chemical  changes  is  always  a  very  important 
circumstance,  and  can  sometimes  be  measured,  and  per- 
haps reduced  to  laws ;  are  we  prohibited  from  speculat- 
ing concerning  the  causes  of  such  circumstances  and 

*  The  Rev.  "W.  Vernon  Harcourt,  Address  to  the  British  Asso- 
ciation, 1839. 

2  D  2 


404  PHILOSOPHY  OF  CHEMISTRY. 

such  laws  ?  And  to  this  we  reply,  that  we  may  properly 
attempt  to  connect  chemical  with  thermotical  processes, 
so  far  as  we  have  obtained  a  clear  and  probable  view  of 
the  nature  of  the  thermotical  processes.  When  our 
theory  of  thermotics  is  tolerably  complete  and  certain, 
we  may  with  propriety  undertake  to  connect  it  with  our 
theory  of  chemistry.  But  at  present  we  are  not  far 
enough  advanced  in  our  knowledge  of  heat  to  make  this 
attempt  with  any  hope  of  success.  We  can  hardly 
expect  to  understand  the  part  which  heat  plays  in  the 
union  of  two  bodies,  when  we  cannot  as  yet  compre- 
hend in  what  manner  it  produces  the  liquefaction  or 
vaporization  of  one  body.  We  cannot  look  to  account 
for  Gay  Lussac  and  Dalton's  Law,  that  all  gases  expand 
equally  by  heat,  till  we  learn  how  heat  causes  a  gas  to 
expand.  We  cannot  hope  to  see  the  grounds  of  Dulong 
and  Petit's  Law,  that  the  specific  heat  of  all  atoms  is 
the  same,  till  we  know  much  more,  not  only  about  atoms, 
but  about  specific  heat.  We  have  as  yet  no  thermotical 
theory  which  even  professes  to  account  for  all  the  pro- 
minent facts  of  the  subject*  :  and  the  theories  which 
have  been  proposed  are  of  the  most  diverse  kind. 
Laplace  assumes  particles  of  bodies  surrounded  by 
atmospheres  of  caloric  f;  Cauchy  makes  heat  consist  in 
longitudinal  vibrations  of  the  ether  of  which  transverse 
vibrations  produce  light:  in  Ampere's  theory  f,  heat 
consists  in  the  vibrations  of  the  particles  of  bodies. 
And  so  long  as  we  have  nothing  more  certain  in  our 
conceptions  of  heat  than  the  alternative  of  these  and 
other  precarious  hypotheses,  how  can  we  expect  to  arrive 
at  any  real  knowledge,  by  connecting  the  results  of  such 
hypotheses  with  the  speculations  of  chemistry,  of  which 
science  the  theory  is  at  least  equally  obscure  ? 

*  Hist.  Ind.  /8W.,  ii.,  530.  f  /£.,  ii.,  531. 

J  /&.,  ii.,  529. 


APPLICATION  OF  THE  IDEA  OF  SUBSTANCE.  405 

The  largest  attempts  at  chemical  theory  have  been 
made  in  the  form  of  the  Atomic  Theory,  to  which  I  have 
just  had  occasion  to  allude.  I  must,  therefore,  before 
quitting  the  subject,  say  a  few  words  respecting  this 
theory. 


CHAPTER  V. 
THE  ATOMIC  THEORY. 

1.  The  Atomic  Theory  considered  on  Chemical 
Grounds. — We  have  already  seen  that  the  combinations 
which  result  from  chemical  affinity  are  definite,  a  certain 
quantity  of  one  ingredient  uniting,  not  with  an  uncertain, 
but  with  a  certain  quantity  of  another  ingredient.  But 
it  was  found,  in  addition  to  this  principle,  that  one  ingre- 
dient would  often  unite  with  another  in  different  propor- 
tions, and  that,  in  such  cases,  these  proportions  are  mul- 
tiples one  of  another.  In  the  three  salts  formed  by 
potassa  with  oxalic  acid,  the  quantities  of  acid  which 
combine  with  the  same  quantity  of  alkali  are  exactly  in 
the  proportion  of  the  numbers  1,  2,  4.  And  the  same 
rule  of  the  existence  of  multiple  proportions  is  found  to 
obtain  in  other  cases. 

It  is  obvious  that  such  results  will  be  accounted  for, 
if  we  suppose  the  base  and  the  acid  to  consist  each  of 
definite  equal  particles,  and  that  the  formation  of  the 
salts  above  mentioned  consists  in  the  combination  of  one 
particle  of  the  base  with  one  particle  of  acid,  with  two 
particles  of  acid,  and  with  four  particles  of  acid,  respec- 
tively. But  further ;  as  we  have  already  stated,  chemical 
affinity  is  not  only  definite,  but  reciprocal.  The  propor- 
tions of  potassa  and  soda  which  form  neutral  salts  are 
590  and  391  in  one  case,  and  therefore  in  all.  These 


406  PHILOSOPHY  OF  CHEMISTRY. 

numbers  represent  the  proportions  of  weight  in  which  the 
two  bases,  potassa  and  soda,  enter  into  analogous  combi- 
nations; 590  of  potassa  is  equivalent  to  391  of  soda. 
These  facts  with  regard  to  combination  are  still  expressed 
by  the  above  supposition  of  equal  particles,  assuming 
that  the  weights  of  a  particle  of  potassa  and  of  soda  are 
in  the  proportion  of  590  to  391. 

But  we  pursue  our  analysis  further.  We  find  that 
potassa  is  a  compound  of  a  metallic  base,  potassium, 
and  of  oxygen,  in  the  proportion  of  490  to  100;  we  sup- 
pose, then,  that  the  particle  of  potassa  consists  of  a  par- 
ticle of  potassium  and  a  particle  of  oxygen,  and  these 
latter  particles,  since  we  see  no  present  need  to  suppose 
them  divided,  potassium  and  oxygen  being  simple  bodies, 
we  may  call  atoms  9  and  assume  to  be  indivisible.  And 
by  supposing  all  simple  bodies  to  consist  of  such  atoms, 
and  compounds  to  be  formed  by  the  union  of  two,  or 
three,  or  more  of  such  atoms,  we  explain  the  occurrence 
of  definite  and  multiple  proportions,  and  we  construct  the 
Atomic  Theory. 

2.  Hypothesis  of  Atoms. — So  far  as  the  assumption 
of  such  atoms  as  we  have  spoken  of  serves  to  express 
those  laws  of  chemical  composition  which  we  have 
referred  to,  it  is  a  clear  and  useful  generalization. 
But  if  the  Atomic  Theory  be  put  forwards  (and  its 
author,  Dr.  Dalton,  appears  to  have  put  it  forwards 
with  such  an  intention,)  as  asserting  that  chemical 
elements  are  really  composed  of  atoms,  that  is,  of  such 
particles  not  further  divisible,  we  cannot  avoid  remark- 
ing, that  for  such  a  conclusion,  chemical  research  has 
not  afforded,  nor  can  afford,  any  satisfactory  evidence 
whatever.  The  smallest  observable  quantities  of  ingre- 
dients, as  well  as  the  largest,  combine  according  to  the 
laws  of  proportions  and  equivalence  which  have  been 
cited  above.  How  are  we  to  deduce  from  such  facts  any 


THE  ATOMIC  THEORY.  407 

inference  with  regard  to  the  existence  of  certain  smallest 
possible  particles?  The  Theory,  when  dogmatically 
taught  as  a  physical  truth,  asserts  that  all  observable 
quantities  of  elements  are  composed  of  proportional 
numbers  of  particles  which  can  no  further  be  subdivided  ; 
but  all  which  observation  teaches  us  is,  that  if  there  be 
such  particles,  they  are  smaller  than  the  smallest  observ- 
able quantities.  In  chemical  experiment,  at  least,  there 
is  not  the  slightest  positive  evidence  for  the  existence  of 
such  atoms.  The  assumption  of  indivisible  particles, 
smaller  than  the  smallest  observable,  which  combine,  par- 
ticle with  particle,  will  explain  the  phenomena ;  but  the 
assumption  of  particles  bearing  this  proportion,  but  not 
possessing  the  property  of  indivisibility,  will  explain  the 
phenomena  at  least  equally  well.  The  decision  of  the 
question,  therefore,  whether  the  Atomic  Hypothesis  be 
the  proper  way  of  conceiving  the  chemical  combinations 
of  substances,  must  depend,  not  upon  chemical  facts,  but 
upon  our  conception  of  substance.  In  this  sense  the 
question  is  an  ancient  and  curious  controversy,  and  we 
shall  hereafter  have  to  make  some  remarks  upon  it. 

3.  Chemical  Difficulties  of  the  Hypothesis.  —  But 
before  doing  this,  we  may  observe  that  there  is  no 
small  difficulty  in  reconciling  this  hypothesis  with  the 
facts  of  chemistry.  According  to  the  theory,  all  salts, 
compounded  of  an  acid  and  a  base,  are  analogous  in  their 
atomic  constitution ;  and  the  number  of  atoms  in  one 
such  compound  being  known  or  assumed,  the  number  of 
atoms  in  other  salts  may  be  determined.  But  when  we 
proceed  in  this  course  of  reasoning  to  other  bodies,  as 
metals,  we  find  ourselves  involved  in  difficulties.  The 
protoxide  of  iron  is  a  base  which,  according  to  all  ana- 
logy, must  consist  of  one  atom  of  iron  and  one  of  oxygen ; 
but  the  peroxide  of  iron  is  also  a  base,  and  it  appears  by 
the  analysis  of  this  substance  that  it  must  consist  of  two- 


408  PHILOSOPHY  OF  CHEMISTRY. 

thirds  of  an  atom  of  iron  and  one  atom  of  oxygen. 
Here,  then,  our  indivisible  atoms  must  be  divisible,  even 
upon  chemical  grounds.  And  if  we  attempt  to  evade 
this  difficulty  by  making  the  peroxide  of  iron  consist  of 
two  atoms  of  iron  and  three  of  oxygen,  we  have  to  make 
a  corresponding  alteration  in  the  theoretical  constitution  of 
all  bodies  analogous  to  the  protoxide ;  and  thus  we  over- 
turn the  very  foundation  of  the  theory.  Chemical  facts, 
therefore,  not  only  do  not  prove  the  Atomic  Theory  as 
a  physical  truth,  but  they  are  not,  according  to  any  modi- 
fication yet  devised  of  the  theory,  reconcilable  with  its 
scheme. 

Nearly  the  same  conclusions  result  from  the  attempts 
to  employ  the  Atomic  Hypothesis  in  expressing  another 
important  chemical  law; — the  law  of  the  combinations 
of  gases  according  to  definite  proportions  of  their  volumes, 
experimentally  established  by  Guy  Lussac*.  In  order 
to  account  for  this  law,  it  has  been  very  plausibly  sug- 
gested that  all  gases,  under  the  same  pressure,  contain 
an  equal  number  of  atoms  in  the  same  space ;  and  that 
when  they  combine,  they  unite  atom  to  atom.  Thus  one 
volume  of  chlorine  unites  with  one  volume  of  hydrogen, 
and  form  hydrochloric  acid  f .  But  then  this  hydro- 
chloric acid  occupies  the  space  of  the  two  volumes;  and 
therefore  the  proper  number  of  particles  cannot  be  sup- 
plied, and  the  uniform  distribution  of  atoms  in  all  gases 
maintained,  without  dividing  into  two  each  of  the  com- 
pound particles,  constituted  of  an  atom  of  chlorine  and 
an  atom  of  hydrogen.  And  thus  in  this  case,  also,  the 
Atomic  Theory  becomes  untenable  if  it  be  understood  to 
imply  the  indivisibility  of  the  atoms. 

In  all  these  attempts  to  obtain  a  distinct  physical 
conception  of  chemical  union  by  the  aid  of  the  Atomic 
Hypothesis,  the  atoms  are  conceived  to  be  associated  by 

*  Hist.  Ind.  Sc.,  iii.,  153.  t  DUMAS,  Phil  Chim,  263. 


THE  ATOMIC  THEORY.  409 

certain  forces  of  the  nature  of  mechanical  attractions. 
But  we  have  already  seen*  that  no  such  mode  of  con- 
ception can  at  all  explain  or  express  the  facts  of  che- 
mical combination ;  and  therefore  it  is  not  wonderful  that 
when  the  Atomic  Theory  attempts  to  give  an  account  of 
chemical  relations  by  contemplating  them  under  such 
an  aspect,  the  facts  on  which  it  grounds  itself  should  be 
found  not  to  authorise  its  positive  doctrines;  and  that 
when  these  doctrines  are  tried  upon  the  general  range 
of  chemical  observation,  they  should  prove  incapable  of 
even  expressing,  without  self-contradiction,  the  laws  of 
phenomena. 

4.  Grounds  of  the  Atomic  Doctrine. — Yet  the  doctrine 
of  atoms,  or  of  substance  as  composed  of  indivisible 
particles,  has  in  all  ages  had  great  hold  upon  the  minds 
of  physical  speculators ;  nor  would  this  doctrine  ever 
have  suggested  itself  so  readily,  or  have  been  maintained 
so  tenaciously,  as  the  true  mode  of  conceiving  chemical 
combinations,  if  it  had  not  been  already  familiar  to  the 
minds  of  those  wiio  endeavour  to  obtain  a  general  view 
of  the  constitution  of  nature.  The  grounds  of  the  assump- 
tion of  the  atomic  structure  of  substance  are  to  be  found 
rather  in  the  idea  of  substance  itself,  than  in  the  experi- 
mental laws  of  chemical  affinity.  And  the  question  of 
the  existence  of  atoms,  thus  depending  upon  an  idea 
which  has  been  the  subject  of  contemplation  from  the 
very  infancy  of  philosophy,  has  been  discussed  in  all  ages 
with  interest  and  ingenuity.  On  this  very  account  it  is 
unlikely  that  the  question,  so  far  as  it  bears  upon  che- 
mistry, should  admit  of  any  clear  and  final  solution.  Still 
it  will  be  instructive  to  look  back  at  some  of  the  opinions 
which  have  been  delivered  respecting  this  doctrine. 

5.  Ancient  Prevalence  of  the  Atomic  Doctrine. — The 
doctrine  that  matter  consists  of  minute,  simple,  indivisible, 

*  See  Chapter  I.  of  this  Book. 


410  PHILOSOPHY  OF  CHEMISTRY. 

indestructible  particles  as  its  ultimate  elements,  has  been 
current  in  all  ages  and  countries,  whenever  the  tendency 
of  man  to  wide  and  subtle  speculations  has  been  active. 
I  need  not  attempt  to  trace  the  history  of  this  opinion  in 
the  schools  of  Greece  and  Italy.  It  was  the  leading 
feature  in  the  physical  tenets  of  the  Epicureans,  and  was 
adopted  by  their  Roman  disciples,  as  the  poem  of  Lucre- 
tius copiously  shows  us.  The  same  tenet  had  been  held 
at  still  earlier  periods,  in  forms  more  or  less  definite,  by 
other  philosophers.  It  is  ascribed  to  Democritus,  and  is 
said  to  have  been  by  him  derived  from  Leucippus.  But 
this  doctrine  is  found  also,  we  are  told*,  among  the 
speculations  of  another  intellectual  and  acute  race,  the 
Hindoos.  According  to  some  of  their  philosophical 
writers,  the  ultimate  elements  of  matter  are  atoms,,  of 
which  it  is  proved  by  certain  reasonings,  that  they  are 
each  one-sixth  of  one  of  the  motes  that  float  in  the 
sunbeam. 

This  early  prevalence  of  controversies  of  the  widest 
and  deepest  kind,  which  even  in  our  day  remain  unde- 
cided, has  in  it  nothing  which  need  surprise  us ;  or,  at 
least,  it  has  in  it  nothing  which  is  not  in  conformity  with 
the  general  course  of  the  history  of  philosophy.  As  soon 
as  any  ideas  are  clearly  possessed  by  the  human  mind,  its 
activity  and  acuteness  in  reasoning  upon  them  are  such, 
that  the  fundamental  antitheses  and  ultimate  difficul- 
ties which  belong  to  them  are  soon  brought  into  view. 
The  Greek  and  Indian  philosophers  had  mastered  com- 
pletely the  Idea  of  Space,  and  possessed  the  Idea  of 
Substance  in  tolerable  distinctness.  They  were,  therefore, 
quite  ready,  with  their  lively  and  subtle  minds,  to  discuss 
the  question  of  the  finite  and  infinite  divisibility  of  matter, 
so  far  as  it  involved  only  the  ideas  of  space  and  of  sub- 

*  By  Mr.  Colebrook.     Asiatic  Res,  ]824. 


THE  ATOMIC  THEORY.  411 

stance,  and  this  accordingly  they  did  with  great  ingenuity 
and  perseverance. 

But  the  ideas  of  Space  and  of  Substance  are  far  from 
being  sufficient  to  enable  men  to  form  a  complete  general 
view  of  the  constitution  of  matter.  We  must  add  to 
these  ideas,  that  of  mechanical  Force  with  its  antagonist 
Resistance,  and  that  of  the  Affinity  of  one  kind  of  matter 
for  another.  Now  the  former  of  these  ideas  the  ancients 
possessed  in  a  very  obscure  and  confused  manner;  and 
of  the  latter  they  had  no  apprehension  whatever.  They 
made  vague  assumptions  respecting  the  impact  and  pres- 
sure of  atoms  on  each  other ;  but  of  their  mutual  attrac- 
tion and  repulsion  they  never  had  any  conception,  except 
of  the  most  dim  and  wavering  kind ;  and  of  an  affinity 
different  from  mere  local  union  they  did  not  even  dream. 
Their  speculations  concerning  atoms,  therefore,  can  have 
no  value  for  us,  except  as  a  part  of  the  history  of  science. 
If  their  doctrines  appear  to  us  to  approach  near  to  the 
conclusions  of  our  modern  philosophy,  it  must  be  because 
our  modern  philosophy  has  not  fully  profited  by  the  addi- 
tional light  which  the  experiments  and  meditations  of 
later  times  have  thrown  upon  the  constitution  of  matter. 

6.  Bacon. — Still,  when  modern  philosophers  look  upon 
the  Atomic  Theory  of  the  ancients  in  a  general  point  of 
view  merely,  without  considering  the  special  conditions 
which  such  a  theory  must  fulfil,  in  order  to  represent  the 
discoveries  of  modern  times,  they  are  disposed  to  regard 
it  with  admiration.  Accordingly  we  find  Francis  Bacon 
strongly  expressing  such  a  feeling.  The  Atomic  Theory  is 
selected  and  dwelt  upon  by  him  as  the  chain  which  connects 
the  best  parts  of  the  physical  philosophy  of  the  ancient 
and  the  modern  world.  Among  his  works  is  a  remarkable 
dissertation  On  the  Philosophy  of  Democritiis,  Parmenides, 
and  Tele-sins;  the  last? mentioned  of  whom  was  one  of 
the  revivers  of  physical  science  in  modern  times.  In 


412  PHILOSOPHY  OF  CHEMISTRY. 

this  work  he  speaks  of  the  atomic  doctrine  of  Democritus 
as  a  favourable  example  of  the  exertions  of  the  undis- 
ciplined intellect.  "Haec  ipsa  placita,  quamvis  paulo 
emendatiora,  talia  sunt  qualia  esse  possunt  ille  quae  ab 
intellectu  sibi  permisso,  nee  continenter  et  gradatim  sub- 
levato,  profecta  videntur." — "  Accordingly,"  he  adds,  "  the 
doctrine  of  Atoms,  from  its  going  a  step  beyond  the 
period  in  which  it  was  advanced,  was  ridiculed  by  the 
vulgar,  and  severely  handled  in  the  disputations  of  the 
learned,  notwithstanding  the  profound  acquaintance  with 
physical  science  by  which  its  author  was  allowed  to  be 
distinguished,  and  from  which  he  acquired  the  character 
of  a  magician." 

"  However,"  he  continues,  "  neither  the  hostility  of 
Aristotle,  with  all  his  skill  and  vigour  in  disputation, 
(though,  like  the  Ottoman  sultans,  he  laboured  to  destroy 
all  his  brother  philosophers  that  he  might  rest  undis- 
puted master  of  the  throne  of  science,)  nor  the  majestic 
and  lofty  authority  of  Plato,  could  effect  the  subversion 
of  the  doctrine  of  Democritus.  And  while  the  opinions 
of  Plato  and  Aristotle  were  rehearsed  with  loud  decla- 
mation and  professorial  pomp  in  the  schools,  this  of 
Democritus  was  always  held  in  high  honour  by  those  of 
a  deeper  wisdom,  who  followed  in  silence  a  severer  path 
of  contemplation.  In  the  days~of  Roman  speculation  it 
kept  its  ground  and  its  favour ;  Cicero  everywhere  speaks 
of  its  author  with  the  greatest  praise ;  and  Juvenal,  who, 
like  poets  in  general,  probably  expressed  the  prevailing 
judgment  of  his  time,  proclaims  his  merit  as  a  noble 
exception  to  the  general  stupidity  of  his  countrymen. 

.     .     .     .     Cujus  prudentia  monstrat 
Magnos  posse  viros  et  magna  exempla  daturos 
Yervecum  in  patria  crassoque  sub  aere  nasci. 

"  The  destruction  of  this  philosophy  was  not  effected 
by  Aristotle  and  Plato,  but  by  Genseric  and  Attila,  and 


THE  ATOMIC  THEORY.  413 

their  barbarians.  For  then,  when  human  knowledge  had 
suffered  shipwreck,  those  fragments  of  the  Aristotelian 
and  Platonic  philosophy  floated  on  the  surface  like  things 
of  some  lighter  and  emptier  sort,  and  so  were  preserved ; 
while  more  solid  matters  went  to  the  bottom,  and  were 
almost  lost  in  oblivion." 

7.  Modern  Prevalence  of  the  Atomic  Doctrine. — It  is 
our  business  here  to  consider  the  doctrine  of  Atoms  only 
in  its  bearing  upon  existing  physical  sciences,  and  I  must 
therefore  abstain  from  tracing  the  various  manifestations 
of  it  in  the  schemes  of  hypothetical  cosmologists ; — its 
place  among  the  vortices  of  Descartes,  its  exhibition  in 
the  monads  of  Leibnitz.  I  will,  however,  quote  a  passage 
from  Newton  to  show  the  hold  it  had  upon  his  mind. 

At  the  close  of  his  Opticks  he  says,  "  All  these  things 
being  considered,  it  seems  probable  to  me  that  God,  in 
the  beginning,  formed  matter  in  solid,  massy,  hard, 
impenetrable,  moveable  particles,  of  such  sizes  and 
figures,  and  with  such  other  properties,  and  in  such  pro- 
portions to  space,  as  most  conduced  to  the  end  for  which 
He  formed  them;  and  that  these  primitive  particles, 
being  solids,  are  incomparably  harder  than  any  porous 
bodies  compounded  of  them,  even  so  very  hard  as  never 
to  wear  or  break  in  pieces ;  no  ordinary  power  being  able 
to  divide  what  God  had  made  one  in  the  first  creation. 
While  the  particles  continue  entire,  they  may  compose 
bodies  of  one  and  the  same  nature  and  texture  in  all 
ages :  but  should  they  wear  away  or  break  in  pieces,  the 
nature  of  things  depending  on  them  would  be  changed. 
Water  and  earth  composed  of  old  worn  particles  and 
fragments  of  particles  would  not  be  of  the  same  nature 
and  texture  now  with  water  and  earth  composed  of  entire 
particles  in  the  beginning.  And  therefore  that  nature 
may  be  lasting,  the  changes  of  corporeal  things  are  to  be 
placed  only  in  the  various  separations  and  new  associa- 


414  PHILOSOPHY  OF  CHEMISTRY. 

tions  and  motions  of  these  permanent  particles;  com- 
pounded bodies  being  apt  to  break,  not  in  the  midst  of 
solid  particles,  but  where  those  particles  are  laid  together 
and  only  touch  in  a  few  points." 

We  shall  hereafter  see  how  extensively  the  atomic 
doctrine  has  prevailed  among  still  more  recent  philoso- 
phers. Not  only  have  the  chemists  assumed  it  as  the 
fittest  form  for  exhibiting  the  principles  of  multiple  pro- 
portions ;  but  the  physical  mathematicians,  as  Laplace  and 
Poisson,  have  made  it  the  basis  of  their  theories  of  heat, 
electricity,  capillary  action;  and  the  crystallographers 
have  been  supposed  to  have  established  both  the  exist- 
ence and  the  arrangement  of  such  ultimate  molecules. 

In  the  way  in  which  it  has  been  employed  by  such 
writers,  the  hypothesis  of  ultimate  particles  has  been  of 
great  use,  and  is  undoubtedly  permissible.  But  when  we 
would  assert  this  theory,  not  as  a  convenient  hypothesis 
for  the  expression  or  calculation  of  the  laws  of  nature, 
but  as  a  philosophical  truth  respecting  the  constitution 
of  the  universe,  we  find  ourselves  checked  by  difficulties 
of  reasoning  which  we  cannot  overcome,  as  wrell  as  by 
conflicting  phenomena  which  we  cannot  reconcile.  I 
will  attempt  to  state  briefly  the  opposing  arguments  on 
this  question. 

8.  Arguments  for  and  against  Atoms. — The  leading 
arguments  on  the  two  sides  of  the  question,  in  their  most 
general  form,  may  be  stated  as  follows : — 

For  the  Atomic  Doctrine. — The  appearances  which 
nature  presents  are  compounded  of  many  parts,  but  if  we 
go  on  resolving  the  larger  parts  into  smaller,  and  so  on 
successively,  we  must  at  last  come  to  something  simple. 
For  that  which  is  compound  can  be  so  no  otherwise  than 
by  composition  of  what  is  simple ;  and  if  we  suppose  all 
composition  to  be  removed,  which  hypothetically  we  may 
do,  there  can  remain  nothing  but  a  number  of  simple 


THE  ATOMIC  THEORY.  415 

substances,  capable  of  composition,  but  themselves  not 
compounded.  That  is,  matter  being  dissolved,  resolves 
itself  into  atoms. 

Against  the  Atomic  Doctrine. — Space  is  divisible 
without  limit,  as  may  be  proved  by  geometry ;  and  matter 
occupies  space,  therefore  matter  is  divisible  without  limit, 
and  no  portion  of  matter  is  indivisible,  or  an  atom. 

And  to  the  argument  on  the  other  side  just  stated,  it 
is  replied  that  we  cannot  even  hypothetically  divest  a  body 
of  composition,  if  by  composition  we  mean  the  relation  of 
point  to  point  in  space.  However  small  be  a  particle,  it 
is  compounded  of  parts  having  relation  in  space. 

The  Atomists  urge  again,  that  if  matter  be  infinitely 
divisible,  a  finite  body  consists  of  an  infinite  number  of 
parts,  which  is  a  contradiction.  To  this  it  is  replied,  that 
the  finite  body  consists  of  an  infinite  number  of  parts  in 
the  same  sense  in  which  the  parts  are  infinitely  small, 
which  is  no  contradiction. 

But  the  opponents  of  the  Atomists  not  only  rebut, 
but  retort  this  argument  drawn  from  the  notion  of 
infinity.  Your  atoms,  they  say,  are  indivisible  by  any 
finite  force ;  therefore  they  are  infinitely  hard ;  and  thus 
your  finite  particles  possess  infinite  properties.  To  this 
the  Atomists  are  wont  to  reply,  that  they  do  not  mean 
the  hardness  of  their  particles  to  be  infinite,  but  only  so 
great  as  to  resist  all  usual  natural  forces.  But  here  it  is 
plain  that  their  position  becomes  untenable ;  for,  in  the 
first  place,  their  assumption  of  this  precise  degree  of 
hardness  in  the  particles  is  altogether  gratuitous ;  and  in 
the  next  place,  if  it  were  granted,  such  particles  are  not 
atoms,  since  in  the  next  moment  the  forces  of  nature 
may  be  augmented  so  as  to  divide  the  particle,  though 
hitherto  undivided. 

Such  are  the  arguments  for  and  against  the  Atomic 
Theory  in  its  original  form.  But  when  these  atoms  are 


416  PHILOSOPHY  OF  CHEMISTRY. 

conceived,  as  they  have  been  by  Newton,  and  commonly 
by  his  followers,  to  be  solid,  hard  particles  exerting 
attractive  and  repulsive  forces,  a  new  set  of  arguments 
come  into  play.  Of  these,  the  principal  one  may  be  thus 
stated :  According  to  the  Atomic  Theory  thus  modified, 
the  properties  of  bodies  depend  upon  the  attractions  and 
repulsions  of  the  particles.  Therefore,  among  other  pro- 
perties of  bodies,  their  hardness  depends  upon  such  forces. 
But  if  the  hardness  of  the  bodies  depends  upon  the  forces, 
the  repulsion,  for  instance,  of  the  particles,  upon  what 
does  the  hardness  of  the  particles  depend  ?  what  progress 
do  we  make  in  explaining  the  properties  of  bodies,  when 
we  assume  the  same  properties  in  our  explanation?  and 
to  what  purpose  do  we  assume  that  the  particles  are  hard  ? 

9.  Transition  to  Boscovictis  Theory. — To  this  diffi- 
culty it  does  not  appear  easy  to  offer  any  reply.  But 
if  the  hardness  and  solidity  of  the  particles  be  given 
up  as  an  incongruous  and  untenable  appendage  to 
the  Newtonian  view  of  the  Atomic  Theory,  we  are  led 
to  the  theory  of  Boscovich,  according  to  which  matter 
consists  not  of  solid  particles,  but  of  mere  mathematical 
centres  of  force.  According  to  this  theory,  each  body  is 
composed  of  a  number  of  geometrical  points  from  which 
emanate  forces,  following  certain  mathematical  laws  in 
virtue  of  which  they  become,  at  certain  small  distances 
attractive,  at  certain  other  distances  repulsive,  and  at 
greater  distances  attractive  again.  From  these  forces  of 
the  points  arise  the  cohesion  of  the  parts  of  the  same 
body,  the  resistance  which  it  exerts  against  the  pressure 
of  another  body,  and  finally  the  attraction  of  gravitation 
which  it  exerts  upon  bodies  at  a  distance. 

This  theory  is  at  least  a  homogeneous  and  consistent 
mechanical  theory,  and  it  is  probable  that  it  may  be  used 
as  an  instrument  for  investigating  and  expressing  true 
laws  of  nature ;  although,  as  we  have  already  said,  the 


THE  ATOMIC  THEORY.  417 

attempt  to  identify  the  forces  by  which  the  particles  of 
bodies  are  bound  together  with  mechanical  attraction 
appears  to  be  a  confusion  of  two  separate  ideas. 

10.  Use  of  the  Molecular  Hypothesis. — In  this  form, 
representing  matter  as  a  collection  of  molecules  or 
centres  of  force,  the  Atomic  Theory  has  been  abundantly 
employed  in  modern  times  as  an  hypothesis  on  which 
calculations  respecting  the  elementary  forces  of  bodies 
might  be  conducted.  When  thus  employed  it  is  to  be 
considered  as  expressing  the  principle  that  the  properties 
of  bodies  depend  upon  forces  emanating  from  immovable 
points  of  their  mass.  This  view  of  the  way  in  which  the 
properties  of  bodies  are  to  be  treated  by  the  mechanical 
philosopher  was  introduced  by  Newton,  and  was  a  natural 
sequel  to  the  success  which  he  had  obtained  by  reasoning 
concerning  central  forces  on  a  large  scale.  I  have 
already  quoted  his  Preface  to  the  Principia,  in  which  he 
says,  "  Many  things  induce  me  to  believe  that  the  rest 
of  the  phenomena  of  nature,  as  well  as  those  of  astro- 
nomy, may  depend  upon  certain  forces  by  which  the 
particles  of  bodies,  in  virtue  of  causes  not  yet  known,  are 
urged  towards  each  other  and  cohere  in  regular  figures, 
or  are  mutually  repelled  and  recede ;  and  philosophers, 
knowing  nothing  of  these  forces,  have  hitherto  failed  in 
their  examination  of  nature."  Since  the  time  of  Newton, 
this  line  of  speculation  has  been  followed  with  great 
assiduity,  and  by  some  mathematicians  with  great  success. 
In  particular  Laplace  has  shown  that  it  may,  in  many 
instances,  be  made  a  much  closer  representation  of 
nature,  if  we  suppose  the  forces  exerted  by  the  particles 
to  deciease  so  rapidly  with  the  increasing  distance  from 
them,  that  the  force  is  finite  only  at  distances  impercep- 
tible to  our  senses,  and  vanishes  at  all  remoter  points. 
He  has  taught  the  method  of  expressing  and  calculating 
such  forces,  and  he  and  other  mathematicians  of  his 
VOL.  i.  2  fi 


418  PHILOSOPHY  OP  CHEMISTRY. 

school  have  applied  this  method  to  many  of  the  most 
important  questions  of  physics ;  as  capillary  action,  the 
elasticity  of  solids,  the  conduction  and  radiation  of  heat. 
The  explanation  of  many  apparently"  unconnected  and 
curious  observed  facts  by  these  mathematical  theories  gives 
us  a  strong  assurance  that  its  essential  principles  are  true. 
But  it  must  be  obsei-ved  that  the  actual  constitution 
of  bodies  as  composed  of  distinct  and  separate  particles  is 
by  no  means  proved  by  these  coincidences.  The  assump- 
tion, in  the  reasoning,  of  certain  centres  of  force  acting 
at  a  distance,  is  to  be  considered  as  nothing  more  than  a 
method  of  reducing  to  calculation  that  view  of  the 
constitution  of  bodies,  which  supposes  that  they  exert 
force  at  every  point.  It  is  a  mathematical  artifice  of  the 
same  kind  as  the  hypothetical  division  of  a  body  into 
infinitesimal  parts,  in  order  to  find  its  centre  of  gravity ; 
and  no  more  implies  a  physical  reality  than  that  hypo- 
,  thesis  does* 

11.  Poisson's  Inference. — When,  therefore,  M.  Pois- 
son,  in  his  views  of  Capillary  Action,  treats  this  hypothe- 
tical distribution  of  centres  of  force  as  if  it  were  a 
physical  fact,  and  blames  Laplace  for  not  taking  account 
of  their  different  distribution  at  the  surface  of  the  fluid 
and  below  it*,  he  appears  to  push  the  claims  of  the 
molecular  hypothesis  too  far.  The  only  ground  for  the 
assumption  of  separate  centres,  is  that  we  can  thus  ex- 
plain the  action  of  the  whole  mass.  The  intervals  between 
the  centres  nowhere  enter  into  this  explanation :  and 
therefore  we  can  have  no  reason  for  assuming  these  inter- 
vals different  in  one  part  of  the  fluid  and  in  the  other. 
M  Poisson  asserts  that  the  density  of  the  fluid  diminishes 
when  we  approach  very  near  the  surface ;  but  he  allows 
that  this  diminution  is  not  detected  by  experiment,  and 
that  the  formula}  on  his  supposition,  so  far  as  the  results 

*  POISSON,  Theorle  de  I' Action  Capillaire. 


THE  ATOMIC  THEORY.  419 

go,  are  identical  with  those  of  Laplace.  It  is  clear,  then, 
that  his  doctrine  consists  merely  in  the  assertion  of  the 
necessary  truth  of  a  part  of  the  hypothesis  which  cannot 
be  put  to  the  test  of  experiment.  It  is  true,  that  so  long 
as  we  have  before  us  the  hypothesis  of  separate  centres, 
the  particles  very  near  the  surface  are  not  in  a  condition 
symmetrical  with  that  of  the  others :  but  it  is  also  true 
that  this  hypothesis  is  only  a  step  of  calculation.  There 
results,  at  one  period  of  the  process  of  deduction,  a 
stratum  of  smaller  density  at  the  surface  of  the  fluid ;  but 
at  a  succeeding  point  of  the  reasoning  the  thickness  of 
this  stratum  vanishes ;  it  has  no  physical  existence. 

Thus  the  molecular  hypothesis,  as  used  in  such  cases, 
does  not  differ  from  the  doctrine  of  forces  acting  at  every 
point  of  the  mass ;  and  this  principle,  which  is  common 
to  both  the  opposite  views,  is  the  true  part  of  each. 

12.  WollastorCs  Argument.  —  An  attempt  has  been 
made  in  another  case,  but  depending  on  nearly  the  same 
arguments,  to  bring  the  doctrine  of  ultimate  atoms  to  the 
test  of  observation.  In  the  case  of  the  air,  we  know  that 
there  is  a  diminution  of  density  in  approaching  the  upper 
surface  of  the  atmosphere,  if  it  have  a  surface :  but  it  is 
held  by  some  that  except  we  allow  the  doctrine  of  ulte- 
nate  molecules,  it  will  not  be  bounded  by  any  surface, 
but  will  extend  to  an  infinite  distance.  This  is  the 
reasoning  of  Wollaston*.  "  If  air  consists  of  any  ultimate 
particles  no  longer  divisible,  then  must  the  expansion  of 
the  medium  composed  of  them  cease  at  that  distance 
where  the  force  of  gravity  downwards  is  equal  to  the 
resistance  arising  from  the  repulsive  force  of  the  medium." 
But  if  there  be  no  such  ultimate  particles,  every  stratum 
will  require  a  stratum  beyond  it  to  prevent  by  its  weight 
a  further  expansion,  and  thus  the  atmosphere  must 
extend  to  an  infinite  distance.  And  Wollaston  con- 

*  Phil.  Trans.,  1822,  p.  89. 

2  E  2 


420  PHILOSOPHY  OF  CHEMISTRY. 

ceived  that  he  could  learn  from  observation  whether  the 
atmosphere  was  thus  diffused  through  all  space ;  for  if  so, 
it  must,  he  argued,  be  accumulated  about  the  larger 
bodies  of  the  system,  as  Jupiter  and  the  Sun,  by  the  law 
of  universal  gravitation ;  and  the  existence  of  an  atmo- 
sphere about  these  bodies,  might,  he  remarked,  be  detected 
by  its  effects  in  producing  refraction.  His  result  is,  that 
"  all  the  phenomena  accord  entirely  with  the  supposition 
that  the  earth's  atmosphere  is  of  finite  extent,  limited  by 
the  weight  of  ultimate  atoms  of  definite  magnitude,  no 
longer  divisible  by  repulsion  of  their  parts." 

A  very  little  reflection  will  show  us  that  such  a  line 
of  reasoning  cannot  lead  to  any  result.  For  we  know 
nothing  of  the  law  which  connects  the  density  with  the 
compressing  force,  in  air  so  extremely  rare  as  we  must 
suppose  it  to  be  near  the  boundary  of  the  atmosphere. 
Now  there  are  possible  laws  of  dependence  of  the  den- 
sity upon  the  compressing  force  such  that  the  atmosphere 
would  terminate  in  virtue  of  the  law  without  any  assump- 
tion of  atoms.  This  may  be  proved  by  mathematical  rea- 
soning. If  we  suppose  the  density  of  air  to  be  as  the 
square  root  of  the  compressing  force,  it  will  follow  that  at 
the  very  limits  of  the  atmosphere,  the  strata  of  equal 
thickness  may  observe  in  their  densities  such  a  law  of 
proportion  as  is  expressed  by  the  numbers  7,  5,  3, 1  *. 

If  it  be  asked  how,  on  this  hypothesis,  the  density  of 
the  highest  stratum  can  be  as  1,  since  there  is  nothing  to 

*  For  the  compressing  force  on  each  being  as  the  whole  weight 
beyond  it,  will  be  for  the  four  highest  strata,  16,  9.  4  and  1,  of  which 
the  square  roots  are  as  4,  3,  2,  1,  or,  as  8,  6,  4,  2 ;  and  though  these 
numbers  are  not  exactly  as  the  densities  7,  5,  3,  1,  those  who  are 
a  little  acquainted  with  mathematical  reasoning,  will  see  that  the  dif- 
ference arises  from  taking  so  small  a  number  of  strata.  If  we  were  to 
make  the  strata  indefinitely  thin,  as  to  avoid  error  we  ought  to  do,  the 
coincidence  would  be  exact ;  and  thus,  according  to  this  law,  the  series 
of  strata  terminates  as  we  ascend,  without  any  consideration  of  atoms. 


THE   ATOMIC   THEORY.  421 

compress  it,  we  answer  that  the  upper  part  of  the  highest 
stratum  compresses  the  lower,  and  that  the  density  dimi- 
nishes continually  to  the  surface,  so  that  the  need  of 
compression  and  the  compressing  weight  vanish  together. 

The  fallacy  of  concluding  that  because  the  height  of 
the  atmosphere  is  finite,  the  weight  of  the  highest  stratum 
must  be  finite,  is  just  the  same  as  the  fallacy  of  those  who 
conclude  that  when  we  project  a  body  vertically  upwards, 
because  it  occupies  only  a  finite  time  in  ascending  to  the 
highest  point,  the  velocity  at  the  last  instant  of  the 
ascent  must  be  finite.  For  it  might  be  said,  if  the  last 
velocity  of  ascent  be  not  finite,  how  can  the  body  describe 
the  last  particle  of  space  in  a  finite  time  ?  and  the  answer 
is,  that  there  is  no  last  finite  particle  of  space,  and  there 
fore  no  last  finite  velocity. 

13.  Permanence  of  Properties  of  Bodies. — We  nave 
already  seen  that,  in  explaining  the  properties  of  mattei 
as  we  find  them  in  nature,  the  assumption  of  solid,  hard, 
indestructible  particles  is  of  no  use  or  value.  But  we 
may  remark,  before  quitting  the  subject,  that  Newton 
appears  to  have  had  another  reason  for  assuming  such 
particles,  and  one  well  worthy  of  notice.  He  wished  to 
express,  by  means  of  this  hypothesis,  the  doctrine  that 
the  laws  of  nature  do  not  alter  with  the  course  of  time. 
This  we  have  already  seen  in  the  quotation  from  Newton. 
"  The  ultimate  particles  of  matter  are  indestructible, 
unalterable,  impenetrable;  for  if  they  could  break  or 
wear,  the  structure  of  material  bodies  now  would  be  dif- 
ferent from  that  which  it  was  when  the  particles  were 
new."  No  philosopher  will  deny  the  truth  which  is  thus 
conveyed  by  the  assertion  of  atoms ;  but  it  is  obviously 
equally  easy  for  a  person  who  rejects  the  atomic  view,  to 
state  this  truth  by  saying  that  the  forces  which  matter 
exerts  do  not  vary  with  time ;  but  however  modified  by 
the  new  modifications  of  its  form,  are  always  unimpaired 


422  PHILOSOPHY  OF  CHEMISTRY. 

in  quantity,  and  capable  of  being  restored  to  their  former 
mode  of  action. 

We  now  proceed  to  speculations  in  which  the  funda- 
mental conceptions  may,  perhaps,  be  expressed,  at  least 
in  some  cases,  by  means  of  the  arrangement  of  atoms ; 
but  in  which  the  philosophy  of  the  subject  appears  to 
require  a  reference  to  a  new  Fundamental  Idea. 


423 


BOOK   VII. 


THE    PHILOSOPHY   OF   MORPHOLOGY, 
INCLUDING  CRYSTALLOGRAPHY. 


CHAPTER  I. 
EXPLICATION  OF  THE  IDEA  OF  SYMMETRY. 

1.  WE  have  seen  in  the  History  of  the  Sciences,  that 
a  principle  which  I  have  there  termed^  the  principle  of 
developed  and  metamorphosed  Symmetry,  has  been  exten- 
sively applied  in  botany  and  physiology,  and  has  given 
rise  to  a  province  of  science  termed  Morphology.  In 
order  to  understand  clearly  this  principle,  it  is  necessary 
to  obtain  a  clear  idea  of  the  Symmetry  of  which  we  thus 
speak.  But  this  Idea  of  Symmetry  is  applicable  in  the 
inorganic,  as  well  as  in  the  organic  kingdoms  of  nature ; 
it  is  presented  to  our  eyes  in  the  forms  of  minerals,  as 
well  as  of  flowers  and  animals ;  we  must,  therefore,  take 
it  under  our  consideration  here,  in  order  that  we  may 
complete  our  view  of  mineralogy,  which,  as  I  have 
repeatedly  said,  is  an  essential  part  of  chemical  science. 
I  shall  accordingly  endeavour  to  unfold  the  Idea  of  Sym- 
metry with  which  we  here  have  to  do. 

It  will  of  course  be  understood  that  by  the  term  Sym- 
metry I  here  intend,  not  that  more  indefinite  attribute  of 
form  which  belongs  to  the  domain  of  the  fine  arts,  as 
when  we  speak  of  the  symmetry  of  an  edifice  or  of  a 

*  Hist.  Ind.  Sci,  iii,,  433. 


424  PHILOSOPHY   OF   MORPHOLOGY. 

sculptured  figure,  but  a  certain  definite  relation  or  pro- 
perty, no  less  rigorous  and  precise  than  other  relations  of 
number  and  position,  which  is  thus  one  of  the  sure  guides 
of  the  scientific  faculty,  and  one  of  the  bases  of  our  exact 
science. 

2.  In  order  to  explain  what  Symmetry  is  in  this  sense, 
let  the  reader  recollect  that  the  bodies  of  animals  consist 
of  two  equal  and  similar  sets  of  members,  the  right  and 
the  left  side ; — that  some  flowers  consist  of  three  or  of  five 
equal  sets  of  organs,  similarly  and  regularly  disposed,  as 
the  iris  has  three  straight  petals,  and  three  reflexed  ones, 
alternately  disposed,  the  rose  li&sjive  equal  and  similar 
sepals  of  the  calyx,  and  alternate  with  these  as  many 
petals  of  the  corolla.  This  orderly  and  exactly  similar 
distribution  of  two,  or  three,  or  five,  or  any  other  number 
of  parts,  is  Symmetry ;  and  according  to  its  various  modi- 
fications, the  forms  thus  determined  are  said  to  be  sym- 
metrical with  various  numbers  of  members.  The  classifi- 
cation of  these  different  kinds  of  symmetry  has  been 
most  attended  to  in  Crystallography,  in  which  science  it 
is  the  highest  and  most  general  principle  by  which  the 
classes  of  forms  are  governed.  Without  entering  far 
into  the  technicalities  of  the  subject,  we  may  point  out 
some  of  the  features  of  such  classes. 

The  first  of  the  figures(l)  in  the 
margin  may  represent  the  summit 
of  a  crystal  as  it  appears  to  an  eye 
looking  directly  down  upon  it ; 
the  centre  of  the  figure  repre- 
sents the  summit  of  a  pyramid,  and  the  spaces  of  various 
forms  which  diverge  from  this  point  represent  sloping  sides 
of  the  pyramid.  Now  it  will  be  observed  that  the  figure 
consists  of  three  portions  exactly  similar  to  one  another, 
and  that  each  part  or  member  is  repeated  in  each  of  these 
portions.  The  faces,  or  pairs  of  faces,  are  repeated  in 


EXPLICATION  OF  THE  IDEA  OF  SYMMETRY. 


425 


threes,  with  exactly  similar  forms  and  angles.    This  figure  is 
said  to  be  three-membered,  or  to  have  triangular  symmetry. 
The  same  kind  of  symmetry  may  exist  in  a  flower,  as  pre- 
sented in  the  accompanying  figure,  and  does,  in  fact,  occur 
in  a  large  class  of  flowers,  as  for  example,  all  the  lily  tribe. 
The  next  pair  of  figures  (2)  have  four  equal  and  similar 
portions,  and  have  their  members 
or  pairs  of  members  four  times  re- 
peated.    Such  figures  are  termed 
four-membered,  and  are   said  to 
have  square  or  tetragonal  symme- 
try.    The  pentagonal  symmetry, 
formed  by  five  similar  members, 
is  represented  in  the  next  figures 
(B).    It  occurs  abundantly  in  the 
vegetable  world,  but  never  among 
crystals;    for  the  pentagonal  fi- 
gures which   crystals   sometimes 
assume,  are  never  exactly  regular. 
But  there  is  still  another  kind  of 
symmetry  (4)  in  which  the  oppo- 
site   ends  are  exactly  similar  to 
each  other  and  also  the  opposite 
sides ;  this  is  oblong,  or  two-and- 
two-membered    symmetry.     And 
finally,  we  have  the  case  of  sim- 
ple symmetry  (5)   in  which  the 
two  sides  of  the  object  are  ex- 
actly alike  (in  opposite  positions) 
without  any  further  repetition. 

3.  These  different  kinds  of  symmetry  occur  in  various 
ways  in  the  animal,  vegetable,  and  mineral  kingdom;  thus 
vertebrate  animals  have  a  right  and  a  left  side  exactly 
alike  and  thus  possess  simple  symmetry.  The  same  kind 
of  symmetry  (simple  symmetry)  occurs  very  largely  in  the 
forms  of  vegetables,  as  in  most  leaves,  in  papilionaceous, 


426  PHILOSOPHY   OF   MORPHOLOGY. 

personate,  and  labiate  flowers.     Among  minerals,  crystals 
which  possess  this  symmetry  are  called  oblique-prismatic, 
and  are  of  very  frequent  occurrence.      The  oblong,   or 
two-and-two  membered  symmetry  belongs  to  right-prismatic 
crystals ;    and   may  be  seen  in  cruciferous  flowers,   for 
though  these  are  cross-shaped,  the  cross  has  two  longer 
and  two  shorter  arms,  or  pairs  of  arms.     The  square  or 
tetragonal  symmetry  occurs   in  crystals  abundantly ;    to 
the   vegetable  world  it  appears  to  be   less    congenial; 
for  though  there  are  flowers  with  four  exactly  similar 
and  regularly-disposed  petals,  as  the  herb   Paris  (Paris 
quadrifolia),  these  flowers  appear,  from  various   circum- 
stances, to  be  deviations  from  the  usual  type  of  vege- 
table forms.     The  trigonal,  or  tJiree-membered  symmetry  is 
found  abundantly  both  in  plants  and  in  crystals,  while  the 
pentagonal  symmetry,  on  the  other  hand,  though  by  far 
the  most  common  among   flowers,    nowhere    occurs  in 
minerals,  and  does  not  appear  to  be  a  possible  form  of 
crystals.     This  pentagonal  form  further  occurs  in  the  ani- 
mal kingdom,  which  the  oblong,  triangular,  and  square 
forms  do  not.     Many  of  Cuvier's  radiate  animals  appear 
in  this  pentagonal  form,  as  echini  and  pentacrin ites,  which 
latter  have  hence  their  name. 

4.  The  regular,  or  as  they  may  be  called,  the  normal 
types  of  the  vegetable  world  appear  to  be  the  forms  which 
possess  triangular  and  pentagonal  symmetry ;  from  these 
the  others  may  be  conceived  to  be  derived,  by  transforma- 
tions resulting  from  the  expansion  of  one  or  more  parts. 
Thus  it  is  manifest  that  if  in  a  three-membered  or  five- 
membered  flower,  one  of  the  petals  be  expanded  more 
than  the  other,  it  is  immediately  reduced  from  pentagonal 
or  trigonal,  to  simple  symmetry.  And  the  oblong  or  two- 
and-two-membered  symmetry  of  the  flowers  of  crucife- 
rous plants,  (in  which  the  stamens  are  four  large  and  two 
small  ones,  arranged  in  regular  opposition,)  is  held  by 


EXPLICATION  OF  THE  IDEA  OF  SYMMETRY.  427 

botanists  to  result  from  a  normal  form  with  ten  stamens ; 
Meinecke  explaining  this  by  adhesion,  and  Sprengel  by 
the  metamorphosis  of  the  stamens  into  petals*. 

It  is  easy  to  see  that  these  various  kinds  of  symmetry 
include  relations  both  of  form  and  of  number,  but  more 
especially  of  the  latter  kind ;  and  as  this  symmetry  is 
often  an  important  character  in  various  classes  of  natural 
objects,  such  classes  have  often  curious  numerical  pro- 
perties. One  of  the  most  remarkable  and  extensive  of 
these  is  the  distinction  which  prevails  between  mono- 
cotyledonous  and  dicotyledonous  plants ;  the  number  three 
being  the  ground  of  the  symmetry  of  the  former,  and  the 
number  Jive,  of  the  latter.  Thus  liliaceous  and  bulbous 
plants,  and  the  like,  have  flowers  of  three  or  six  petals, 
and  the  other  organs  follow  the  same  numbers:  while 
the  vast  majority  of  plants  are  pentandrous,  and  with  their 
five  stamens  have  also  their  other  parts  in  fives.  This 
great  numerical  distinction  corresponding  to  a  leading 
difference  of  physiological  structure  cannot  but  be  con- 
sidered as  a  highly  curious  fact  in  phytology.  Such 
properties  of  numbers,  thus  connected  in  an  incompre- 
hensible manner  with  fundamental  and  extensive  laws 
of  nature,  give  to  numbers  an  appearance  of  myste- 
rious importance  and  efficacy.  We  learn  from  history 
how  strongly  the  study  of  such  properties,  as  they  are 
exhibited  by  the  phenomena  of  the  heavens,  took  posses- 
sion of  the  mind  of  Kepler ;  perhaps  it  was  this,  which, 
at  an  earlier  period,  contributed  in  no  small  degree  to 
the  numerical  mysticism  of  the  Pythagoreans  in  antiquity, 
and  of  the  Arabians  and  others  in  the  middle  ages.  In 
crystallography,  numbers  are  the  primary  characters  in 
which  the  properties  of  substances  are  expressed ; — they 
appear,  first,  in  that  classification  of  forms  which  depends 
on  the  degree  of  symmetry,  that  is,  upon  the  number  of 
*  SPRENGEL,  Gesch.  d.  Bot.,  ii.,  304. 


428  PHILOSOPHY  OF  MORPHOLOGY. 

correspondencies;  and  next,  in  the  laws  of  derivation, 
which,  for  the  most  part,  appear  to  be  common  in  their 
occurrence  in  proportion  to  the  numerical  simplicity  of 
their  expression.  But  the  manifestation  of  a  governing 
numerical  relation  in  the  organic  world  strikes  us  as  more 
unexpected ;  and  the  selection  of  the  number  five  as  the 
index  of  the  symmetry  of  dicotyledonous  plants  and  radi- 
ated animals,  (a  number  which  is  nowhere  symmetrically 
produced  in  inorganic  bodies,)  makes  this  a  new  and 
remarkable  illustration  of  the  constancy  of  numerical  rela- 
tions. We  may  observe,  however,  that  the  moment  one 
of  these  radiate  animals  has  one  of  its  five  members 
expanded,  or  in  any  way  peculiarly  modified,  (as  happens 
among  the  echini)  it  is  reduced  to  the  common  type  of 
animals  simply  symmetrical,  with  a  right  and  left  side. 

5.  It  is  not  necessary  to  attempt  to  enumerate  all  the 
kinds  of  Symmetry,  since  our  object  is  only  to  explain 
what  Symmetry  is,  and  for  this  purpose  enough  has 
probably  been  said  already.  It  will  be  seen,  as  soon  as 
the  notion  of  Symmetry  in  general  is  well  apprehended, 
that  it  is  or  includes  a  peculiar  Fundamental  Idea,  not 
capable  of  being  resolved  into  any  of  the  ideas  hitherto 
examined.  It  may  be  said,  perhaps,  that  the  Idea  of 
Symmetry  is  a  modification  or  derivative  of  our  ideas  of 
space  and  number; — that  a  symmetrical  shape  is  one 
which  consists  of  parts  exactly  similar,  repeated  a  certain 
number  of  times,  and  placed  so  as  to  correspond  with 
each  other.  But  on  further  reflection  it  will  be  seen 
that  this  repetition  and  correspondence  of  parts  in  sym- 
metrical figures  are  something  peculiar ;  for  it  is  not  any 
repetition  or  any  correspondence  of  parts  to  which  we 
should  give  the  name  of  symmetry,  in  the  manner  in 
which  we  are  now  using  the  term.  Symmetrical  arrange- 
ments may  no  doubt  be  concerned  with  space  and"  posi- 
tion, time  and  number ;  but  there  appears  to  be  implied 


EXPLICATION  OF  THE  IDEA  OF  SYMMETRY.  429 

in  them  a  Fundamental  Idea  of  regularity,  of  complete- 
ness, of  complex  simplicity,  which  is  not  a  mere  modifica- 
tion of  other  ideas. 

6.  It  is,  however,  not  necessary,  in  this  and  in  similar 
cases  to  determine  whether  the  idea  which  we  have 
before  us  be  a  peculiar  and  independent  Fundamental 
Idea  or  a  modification  of  other  ideas,  provided  we  clearly 
perceive  the  evidence  of  those  Axioms  by  means  of  which 
the  Idea  is  applied  in  scientific  reasonings.  Now  in  the 
application  of  the  Idea  of  Symmetry  to  crystallography, 
phytology  and  zoology,  we  must  have  this  idea  embodied 
in  some  principle  which  asserts  more  than  a  mere  geome- 
trical or  numerical  accordance  of  members.  We  must 
have  it  involved  in  some  vital  or  productive  action,  in 
order  that  it  may  connect  and  explain  the  facts  of  the 
organic  world.  Nor  is  it  difficult  to  enunciate  such  a 
principle.  We  may  state  it  in  this  manner.  All  the 
symmetrical  members  of  a  natural  product  are,  under  like 
circumstances,  alike  affected.  The  parts  which  we  have 
termed  symmetrical,  resemble  each  other,  not  only  in 
their  form  and  position,  but  also  in  the  manner  in  which 
they  are  produced  and  modified  by  natural  causes.  And 
this  principle  we  assume  to  be  necessarily  true,  however 
unknown  and  inconceivable  may  be  the  causes  which 
determine  the  phenomena.  Thus  it  has  not  yet  been 
found  possible  to  discover  or  represent  to  ourselves,  in 
any  intelligible  manner,  the  forces  by  which  the  various 
faces  of  a  crystal  are  consequent  upon  its  primary  form ; 
but  the  whole  of  crystallography  rests  upon  this  principle, 
that  if  one  of  the  primary  planes  or  axes  be  modified  in 
any  manner,  all  the  symmetrical  planes  and  axes  must  be 
modified  in  the  same  manner.  And  though  accidental 
mechanical  or  other  causes  may  interfere  with  the  actual 
exhibition  of  such  faces,  we  do  not  the  less  assume  their 
crystallographical  reality,  as  inevitably  implied  in  the 


430  PHILOSOPHY  OF  MORPHOLOGY. 

law  of  symmetry  of  the  crystal*.  And  we  apply  similar 
considerations  to  organized  beings.  We  assume  that  in 
a  regular  flower,  each  of  the  similar  members  has  the 
same  organization  and  similar  powers  of  developement ; 
and  hence  if  among  these  similar  parts  some  are  much 
less  developed  than  others,  we  consider  them  as  abortive ; 
and  if  we  wish  to  remove  doubts  as  to  what  are  symme- 
trical members  in  such  a  case,  we  make  the  inquiry  by 
tracing  the  anatomy  of  these  members,  or  by  following 
them  in  their  earlier  states  of  developement,  or  in  cases 
where  their  capabilities  are  magnified  by  monstrosity  or 
otherwise.  The  power  of  developement  may  be  modified 
by  external  causes,  and  thus  we  may  pass  from  one  kind 
of  symmetry  to  another ;  as  we  have  already  remarked. 
Thus  a  regular  flower  with  pentagonal  symmetry,  growing 
on  a  lateral  branch,  has  one  petal  nearest  to  the  axis  of 
the  plant :  if  this  petal  be  more  or  less  expanded  than  the 
others,  the  pentagonal  symmetry  is  interfered  with,  and 
the  flower  may  change  to  a  symmetry  of  another  kind. 
But  it  is  easy  to  see  that  all  such  conceptions  of  expan- 
sion, abortion,  and  any  other  kind  of  metamorphosis  go, 
upon  the  supposition  of  identical  faculties  and  tendencies 
in  each  similar  member,  in  so  far  as  such  tendencies  have 
any  relation  to  the  symmetry.  And  thus  the  principle  we 
have  stated  above  is  the  basis  of  that  which,  in  the  History, 
we  termed  the  Principle  of  Developed  and  Metamor- 
phosed Symmetry. 

We  shall  not  at  present  pursue  the  other  applications 
of  this  Idea  of  Symmetry,  but  we  shall  consider  some  of 
the  results  of  its  introduction  into  Crystallography. 

*  Some  crystalline  forms,  instead  of  being  holohedral  (provided 
with  their  whole  number  of  faces),  are  hemihedral  (provided  with  only 
half  their  number  of  faces).  But  in  these  hemihedral  forms,  the  half 
of  the  faces  are  still  symmetrically  suppressed. 


431 


CHAPTER  II. 

APPLICATION  OF  THE  IDEA  OF  SYMMETRY 
TO  CRYSTALS. 

1.  MINERALS  and  other  bodies  of  definite  chemical 
composition  often  exhibit  that  marked  regularity  of  form 
and  structure  which  we  designate  by  terming  them 
Crystals;  and  in  such  crystals,  when  we  duly  study  them, 
we  perceive  the  various  kinds  of  symmetry  of  which  we 
have  spoken  in  the  previous  chapter.  And  the  different 
kinds  of  symmetry  which  we  have  there  described  are 
now  usually  distinguished  from  each  other,  by  writers  on 
crystallography.  Indeed  it  is  mainly  to  such  writers  that 
we  are  indebted  for  a  sound  and  consistent  classification 
of  the  kinds  and  degrees  of  symmetry  of  which  forms  are 
capable.  But  this  classification  was  by  no  means  invented 
as  soon  as  mineralogists  applied  themselves  to  the  study 
of  crystals.  These  first  attempts  to  arrange  crystalline 
forms  were  very  imperfect;  those,  for  example,  of  Lin- 
nreus,  Werner,  Rome  de  Lisle,  and  Haiiy.  The  essays  of 
these  writers  implied  a  classification  at  once  defective 
and  superfluous.  They  reduced  all  crystals  to  one  or 
other  of  certain  fundamental  forms ;  and  this  procedure 
might  have  been  a  perfectly  good  method  of  dividing 
crystalline  forms  into  classes,  if  the  fundamental  forms 
had  been  selected  so  as  to  exemplify  the  different  kinds 
of  symmetry.  But  this  was  not  the  case.  Haiiy's  fun- 
damental or  "  primitive "  forms,  were,  for  instance,  the 
following :  the  parallelepiped,  the  octahedron,  the  tetra- 
hedron, the  regular  hexagonal  prism,  the  rhombic  dodeca- 
hedron, and  the  double  hexagonal  pyramid.  Of  these, 
the  octahedron,  the  tetrahedron,  the  rhombic  dodeca- 
hedron, all  belong  to  the  same  kind  of  symmetry  (the 


432 


PHILOSOPHY  OF  MORPHOLOGY. 


tessular  systems) ;  also  the  hexagonal  prism  and  the 
hexagonal  pyramid  both  belong  to  the  rhombic  system ; 
while  the  parallelepiped  is  so  employed  as  to  include  all 
kinds  of  symmetry. 

It  is,  however,  to  be  recollected  that  Haiiy,  in  his 
selection  of  primitive  forms,  not  only  had  an  eye  to  the 
external  form  of  the  crystal  and  to  its  degree  and 
kind  of  regularity,  but  also  made  his  classification  with 
an  especial  reference  to  the  cleavage  of  the  mineral, 
which  he  considered  as  a  primary  element  in  crystalline 
analysis.  There  can  be  no  doubt  that  the  cleavage  of  a 
crystal  is  one  of  its  most  important  characters:  it  is  a 
relation  of  form  belonging  to  the  interior,  which  is  to  be 
attended  to  no  less  than  the  form  of  the  exterior.  But 
still  the  cleavage  is  to  be  regarded  only  as  determining 
the  degree  of  geometrical  symmetry  of  the  body,  and  not 
as  defining  a  special  geometrical  figure  to  which  the  body 
must  be  referred.  To  have  looked  upon  it  in  the  latter 
light  was  a  mistake  of  the  earlier  crystallographic  specu- 
lators, on  which  we  shall  shortly  have  to  remark. 

2.  I  have  said  that  the  reference  of  crystals  to  primi- 
tive forms  might  have  been  well  employed  as  a  mode  of 
expressing  a  just  classification  of  them.  This  follows  as 
a  consequence  from  the  application  of  the  principle  stated 
in  the  last  chapter,  that  all  symmetrical  members  are  alike 
affected.  Thus  we  may  take  an  upright  triangular  prism 
as  the  representative  of  the  rhombic  system,  and  if  we  then 
suppose  one  of  the  upper  edges  to  be  cut  off,  or  truncated, 
we  must,  by  the  principle  of  symmetry,  suppose  the  other 
two  upper  edges  to  be  truncated  in  precisely  the  same 
manner.  By  this  truncation  we  may  obtain  the  upper  part 
of  a  rhombohedron ;  and  by  truncations  of  the  same  kind, 
symmetrically  affecting  all  the  analogous  parts  of  the 
figure,  we  may  obtain  any  other  form  possessing  three- 
membered  symmetry.  And  the  same  is  true  of  any  of 


IDEA  OF  SYMMETRY  IN  CRYSTALS.  433 

the  other  kinds  of  symmetry,  provided  we  make  a  proper 
selection  of  a  fundamental  form.  And  this  was  really 
the  method  employed  by  Demeste,  Werner,  and  Rome 
de  Lisle.  They  assumed  a  primitive  form,  and  then  con- 
ceived other  forms,  such  as  they  found  in  nature,  to  be 
derived  from  the  primitive  form  by  truncation  of  the 
edges,  acumination  of  the  corners,  and  the  like  processes. 
This  mode  of  conception  was  a  perfectly  just  and  legiti- 
mate expression  of  the  general  idea  of  symmetry. 

3.  The  true  view  of  the  degrees  of  symmetry  was,  as  I 
have  already  said,  impeded  by  the  attempts  which  Haiiy 
and  others  made  to  arrive  at  primitive  forms  by  the  light 
which  cleavage  was  supposed  to  throw  upon  the  structure 
of  minerals.  At  last,  however,  in  Germany,  as  I  have 
narrated  in  the  History  of  Mineralogy*,  Weiss  and  Mohs 
introduced  a  classification  of  forms  implying  a  more  phi- 
losophical principle,  dividing  the  forms  into  Systems ; 
which,  employing  the  terms  of  the  latter  writer,  we  shall 
call  the  tessular,  the  pyramidal  or  square  pyramidal,  the 
prismatic  or  oblong,  and  the  rJiombohedral  systems. 

Of  these  forms,  the  three  latter  may  be  at  once 
referred  to  those  kinds  of  symmetry  of  which  we  have 
spoken  in  the  last  chapter.  The  rhombohedral  system 
has  triangular  symmetry,  or  is  three-membered :  the 
pyramidal  has  square  symmetry,  or  is  four-membered : 
the  prismatic  has  oblong  symmetry,  and  is  two-and-two- 
membered.  But  the  kinds  of  symmetry  which  were 
spoken  of  in  the  former  chapter,  do  not  exhaust  the  idea 
when  applied  to  minerals.  For  the  symmetry  which  was 
there  explained  was  such  only  as  can  be  exhibited  on  a 
surface,  whereas  the  forms  of  crystals  are  solid.  Not 
only  have  the  right  and  left  parts  of  the  upper  surface  of 
a  crystal  relations  to  each  other ;  but  the  upper  surface 

*  Hist.  Ind.  8d.,  iii.  209. 
VOL.  I.  2  F 


434  PHILOSOPHY  OF  MORPHOLOGY. 

and  the  lateral  faces  of  the  crystal  have  also  their  rela- 
tions; they  may  be  different,  or  they  may  be  alike. 
If  we  take  a  cube,  and  hold  it  so  that  four  of  its  faces 
are  vertical,  not  only  are  all  these  four  sides  exactly  simi- 
lar, so  as  to  give  square  symmetry ;  but  also  we  may  turn 
the  cube,  so  that  any  one  of  these  four  sides  shall  become 
the  top,  and  still  the  four  sides  which  are  thus  made 
vertical,  though  not  the  same  which  were  vertical  before, 
are  still  perfectly  symmetrical.  Thus  this  cubical  figure 
possesses  more  than  square  symmetry.  It  possesses 
square  symmetry  in  a  vertical  as  well  as  in  a  horizontal 
sense.  It  possesses  a  symmetry  which  has  the  same 
relation  to  a  cube  which  four-membered  symmetry  has  to 
a  square.  And  this  kind  of  symmetry  is  termed  the 
cubical  or  tessular  symmetry.  All  the  other  kinds  of 
symmetry  have  reference  to  an  axis,  about  which  the  cor- 
responding parts  are  disposed ;  but  in  tessular  symmetry 
the  horizontal  and  vertical  axes  are  also  symmetrical,  or 
interchangeable ;  and  thus  the  figure  may  be  said  to  have 
no  axis  at  all. 

4.  It  has  already  been  repeatedly  stated  that,  by  the 
very  idea  of  symmetry,  all  the  incidents  of  form  must 
affect  alike  all  the  corresponding  parts.  Now  in  crystals 
we  have,  among  these  incidents,  not  only  external  figure, 
but  cleavage,  which  may  be  considered  as  internal  figure. 
Cleavage,  then,  must  conform  to  the  degree  of  symmetry 
of  the  figure.  Accordingly'cleavage,  no  less  than  form,  is 
to  be  attended  to  in  determining  to  what  system  a  mineral 
belongs.  If  a  crystal  were  to  occur  as  a  square  prism  or 
pyramid,  it  would  not  on  that  account  necessarily  belong 
to  the  square  pyramidal  system.  If  it  were  found  that 
it  was  cleavable  parallel  to  one  side  of  the  prism,  but  not 
in  the  transverse  direction,  it  has  only  oblong  symmetry ; 
and  the  equality  of  the  sides  which  makes  it  square  is 
only  accidental. 


IDEA  OF  SYMMETRY  IN  CRYSTALS.  435 

Thus  no  cleavage  is  admissible  in  any  system  of 
crystallization  which  does  not  agree  with  the  degree  of 
symmetry  of  the  system.  On  the  other  hand,  any  cleavage 
which  is  consistent  with  the  symmetry  of  the  system,  is 
(hypothetically  at  least)  allowable.  Thus  in  the  oblong 
prismatic  system  we  may  have  a  cleavage  "parallel  to  one 
side  only  of  the  prism ;  or  parallel  to  both,  but  of  different 
distinctness ;  or  parallel  to  the  two  diagonals  of  the  prism 
but  of  the  same  distinctness ;  or  we  may  have  both  these 
cleavages  together.  In  the  rhombohedral  system,  the 
cleavage  may  be  parallel  to  the  sides  of  the  rhombo- 
hedron,  as  in  Calc  Spar:  or,  in  the  same  system, 
the  cleavage,  instead  of  being  thus  oblique  to  the  axis, 
may  be  along  the  axis  in  those  directions  which  make 
equal  angles  with  each  other :  this  cleavage  easily  gives 
either  a  triangular  or  a  hexagonal  prism.  Again,  in  the 
tessular  system,  the  cleavage  may  be  parallel  to  the  sur- 
face of  the  cube,  which  is  thus  readily  separable  into 
other  cubes,  as  in  Galena ;  or  the  cleavage  may  be  such 
as  to  cut  off  the  solid  angle  of  the  cube,  and  since  there 
are  eight  of  these,  such  cleavage  gives  us  an  octahedron, 
which,  however,  may  be  reduced  to  a  tetrahedron,  by 
rejecting  all  parallel  faces,  as  being  mere  repetitions  of 
the  same  cleavage;  this  is  the  case  with  Fluor  Spar: 
or  the  cube  of  the  tessular  system  may  be  cleavable  in 
planes  which  truncate  all  the  edges  of  the  cube ;  and  as 
these  are  twelve,  we  thus  obtain  the  dodecahedron  with 
rhombic  faces:  this  occurs  in  Zinc  Blende.  And  thus 
we  see  the  origin  of  Hau'y's  various  primitive  forms,  the 
tetrahedron,  octahedron,  and  rhombic  dodecahedron,  all 
belonging  to  the  tessular  system : — they  are,  in  fact,  dif- 
ferent cleavage  forms  of  that  system. 

5.  I  do  not  dwell  upon  other  incidents  of  crystals 
which  have  reference  to  form,  nor  upon  the  lustre,  smooth- 
ness, and  striation  of  the  surfaces.  To  all  such  incidents 

2  F  2 


430  PHILOSOPHY  OF  MORPHOLOGY. 

the  general  principle  applies,  that  similar  parts  are  simi- 
larly affected ;  and  hence  if  any  parts  are  found  to  be 
constantly  and  definitely  different  from  other  parts  of  the 
same  sort,  they  are  not  similar  parts ;  and  the  symmetry 
is  to  be  interpreted  with  reference  to  this  difference. 

We  have  now  to  consider  the  inferences  which  have 
been  drawn  from  these  incidents  of  crystallization,  with 
regard  to  the  intimate  structure  of  bodies. 


CHAPTER  III. 

SPECULATIONS  FOUNDED  UPON  THE 
SYMMETRY  OF  CRYSTALS. 

1.  WHEN  a  crystal,  as,  for  instance,  a  crystal  of  galena, 
(sulphuret  of  lead,)  is  readily  divisible  into  smaller  cubes, 
and  these  into  smaller  ones,  and  so  on  without  limit,  it  is 
very  natural  to  represent  to  ourselves  the  original  cube  as 
really  consisting  of  small  cubical  elements;  and  to  imagine 
that  it  is  a  philosophical  account  of  the  physical  structure 
of  such  a  substance  to  say  that  it  is  made  up  of  cubical 
molecules.  And  when  the  galena  crystal  has  externally 
the  form  of  a  cube,  there  is  no  difficulty  in  such  a  concep- 
tion; for  the  surface  of  the  crystal  is  also  conceived  as 
made  up  of  the  surfaces  of  its  cubical  molecules.  We 
conceive  the  crystal  so  constituted,  as  we  conceive  a  wall 
built  of  bricks. 

But  if,  as  often  happens,  the  galena  crystal  be  an 
octahedron,  a  further  consideration  is  requisite  in  order 
to  understand  its  structure,  pursuing  still  the  same  hypo- 
thesis. The  mineral  is  still,  as  in  the  other  case,  readily 
cleavable  into  small  cubes,  having  their  corners  turned 
to  the  faces  of  the  octahedron.  Therefore  these  faces 
can  no  longer  be  conceived  as  made  up  of  the  faces  of 


SPECULATIONS  ON  THE  SYMMETRY  OF  CRYSTALS.      437 

cubical  elements  of  which  the  whole  is  constituted.  If 
we  suppose  a  pile  of  such  small  cubes  to  be  closely  built 
together,  but  with  decreasing  width  above,  so  as  to  form 
a  pyramid,  the  face  of  such  a  pyramid  will  no  longer  be 
plane ;  it  will  consist  of  a  great  number  of  the  corners 
or  edges  of  the  small  elementary  cubes.  It  would  ap- 
pear at  first  sight,  therefore,  that  such  a  face  cannot 
represent  the  smooth  polished  surface  of  a  crystal. 

But  when  we  come  to  look  more  closely,  this  diffi- 
culty disappears.  For  how  large  are  these  elementary 
cubes  ?  We  cannot  tell,  even  supposing  they  really  have 
any  size.  But  we  know  that  they  must  be,  at  any  rate, 
very  small ;  so  small  as  to  be  inappreciable  by  our  senses, 
for  our  senses  find  no  limit  to  the  divisibility  of  minerals 
by  cleavage.  Hence  the  surface  of  the  pyramid  above 
described  would  not  consist  of  visible  corners  or  edges, 
but  would  be  roughened  by  specks  of  imperceptible  size ; 
or  rather,  by  supposing  these  specks  to  become  still 
smaller,  the  roughness  becomes  smoothness.  And  thus 
we  may  have  a  crystal  with  a  smooth  surface,  made  up  of 
small  cubes  in  such  a  manner  that  their  surfaces  are  all 
oblique  to  the  surface  of  the  crystal. 

Haiiy,  struck  by  some  instances  in  which  the  suppo- 
sition of  such  a  structure  of  crystals  appeared  to  account 
happily  for  several  of  their  relations  and  properties, 
adopted  and  propounded  it  as  a  general  theory.  The 
small  elements,  of  which  he  supposed  crystals  to  be  thus 
built  up,  he  termed  integrant  molecules.  The  form  of 
these  molecules  might  or  might  not  be  the  same  as  the 
primitive  form  with  which  his  construction  was  supposed 
to  begin ;  but  there  was,  at  any  rate,  a  close  connexion 
between  these  forms,  since  both  of  them  were  founded 
on  the  cleavage  of  the  mineral.  The  tenet  that  crystals 
are  constituted  in  the  manner  which  I  have  been  de- 
scribing, I  shall  call  the  Theory  of  Integrant  Molecules, 


438  PHILOSOPHY   OF   MORPHOLOGY. 

and  I  have  now  to  make  some  remarks  on  the  grounds  of 
this  theory. 

2.  In  the  case  of  which  I  have  spoken,  the  mineral 
used  as  the  example,  galena,  readily  splits  into  cubes,  and 
cubes  are  easily  placed  together  so  as  to  fit  each  other, 
and  fill  the  space  which  they  occupy.  The  same  is  the 
case  in  the  mineral  which  suggested  to  Haiiy  his  theory, 
namely,  calc  spar.  The  crystals  of  this  substance  are 
readily  divisible  into  rhombohedrons,  a  form  like  a  brick 
with  oblique  angles ;  and  such  bricks  can  be  built  to- 
gether so  as  to  produce  crystals  of  all  the  immense  varie- 
ties of  form  which  calc  spar  presents.  This  kind  of 
masonry  is  equally  possible  in  many  other  minerals ;  but 
as  we  go  through  the  mineral  kingdom  in  our  survey,  we 
soon  find  cases  which  offer  difficulties.  Some  minerals 
cleave  only  in  two  directions,  some  in  one  only ;  in  such 
cases  we  cannot  by  cleavage  obtain  an  integrant  mole- 
cule of  definite  form;  one  of  its  dimensions,  at  least, 
must  remain  indeterminate  and  arbitrary.  Again,  in 
some  instances,  we  have  more  than  three  different  planes 
of  cleavage,  as  in  fluor  spar,  where  we  have  four.  The 
solid,  bounded  by  four  planes,  is  a  tetrahedron ;  or  if  we 
take  four  pairs  of  parallel  faces,  an  octahedron.  But  if 
we  attempt  to  take  either  of  these  forms  for  our  inte- 
grant molecule,  we  are  met  by  this  difficulty :  that  a  col- 
lection of  such  forms  will  not  fill  space.  Perhaps  this 
difficulty  will  be  more  readily  conceived  by  the  general 
reader  if  it  be  contemplated  with  reference  to  plane 
figures.  It  will  readily  be  seen  that  a  number  of  equal 
squares  may  be  put  together  so  as  to  fill  the  space  which 
they  occupy ;  but  if  we  take  a  number  of  equal  regular 
octagons,  we  may  easily  convince  ourselves  that  no  pos- 
sible arrangement  can  make  them  cover  a  flat  space  with- 
out leaving  blank  spots  between.  In  like  manner  octa- 
hedrons or  tetrahedrons  cannot  be  arranged  in  solid  space 


SPECULATIONS  ON  THE  SYMMETRY  OF  CRYSTALS.       439 

so  as  to  fill  it.  They  necessarily  leave  vacancies.  Hence 
the  structure  of  fluor  spar,  and  similar  crystals,  was  a 
serious  obstacle  in  the  way  of  the  theory  of  integrant 
molecules.  That  theory  had  been  adopted  in  the  first 
instance  because  portions  of  the  crystal,  obtained  by 
cleavage,  could  be  built  up  into  a  solid  mass ;  but  this 
ground  of  the  theory  failed  altogether  in  such  instances 
as  I  have  described,  and  hence  the  theory,  even  upon  the 
representations  of  its  adherents,  had  no  longer  any  claim 
to  assent. 

The  doctrine  of  Integral  Molecules,  however,  was  by 
no  means  given  up  at  once,  even  in  such  instances.  In 
this  and  in  other  subjects,  we  may  observe  that  a  theory, 
once  constructed  and  carried  into  detail,  has  such  a  hold 
upon  the  minds  of  those  who  have  been  in  the  habit  of 
applying  it,  that  they  will  attempt  to  uphold  it  by  intro- 
ducing suppositions  inconsistent  with  the  original  founda- 
tions of  the  theory.  Thus  those  who  assert  the  atomic 
theory,  reconcile  it  with  facts  by  taking  the  halves  of  atoms; 
and  thus  the  theory  of  integrant  molecules  was  maintained 
for  fluor  spar,  by  representing  the  elementary  octahedrons 
of  which  crystals  are  built  up,  as  touching  each  other  only 
by  the  edges.  The  contact  of  surface  with  surface  amongst 
integrant  molecules  had  been  the  first  basis  of  the  theory ; 
but  this  supposition  being  here  inapplicable,  was  replaced 
by  one  which  made  the  theory  no  longer  a  representation 
of  the  facts  (the  cleavages)  but  a  mere  geometrical  con- 
struction. Although,  however,  the  inapplicability  of  the 
theory  to  such  cases  was  thus,  in  some  degree,  disguised 
to  the  disciples  of  Haiiy,  it  was  plain  that,  in  the  face  of 
such  difficulties,  the  Theory  of  Integrant  Molecules  could 
not  hold  its  place  as  a  philosophical  truth.  But  it  still 
answered  the  purpose  (a  very  valuable  one,  and  one  to 
which  crystallography  is  much  indebted,)  of  an  instru- 
ment for  calculating  the  geometrical  relations  of  the  parts 


440  PHILOSOPHY    OF   MORPHOLOGY. 

of  crystals  to  each  other:  for  the  integrant  molecules 
were  supposed  to  be  placed  layer  above  layer,  each  layer 
as  we  ascend,  decreasing  by  a  certain  number  of  mole- 
cules and  rows  of  molecules ;  and  the  calculation  of  these 
laws  of  decrement  was,  in  fact,  the  best  mode  then  known 
of  determining  the  positions  of  the  faces.  The  Theory 
of  Decrements  served  to  express  and  to  determine,  in 
a  great  number  of  the  most  obvious  cases,  the  laws  of 
phenomena  in  crystalline  forms,  though  the  Theory  of 
Integrant  Molecules  could  not  be  maintained  as  a  just 
view  of  the  structure  of  crystals. 

3.  The  Theory  of  Integrant  Molecules,  however,  in- 
volved this  just  and  important  principle :  that  a  true  view 
of  the  intimate  structure  of  crystals  must  include  and 
explain  the  facts  of  crystallization,  that  is,  crystalline 
form  and  cleavage;  and  that  it  must  take  these  into 
account,  according  to  their  degree  of  symmetry.  So  far 
all  theories  concerning  the  elements  of  crystals  must 
agree.  And  it  was  soon  seen  that  this  was,  in  reality,  all 
that  had  been  established  by  the  investigations  of  Haiiy 
and  his  school.  I  have  already,  in  the  History,  quoted 
Weiss's  reflections  on  making  this  step.  "  When  in 
1809,"  he  says*,  "  I  published  my  Dissertation,  I  shared 
the  common  opinion  as  to  the  necessity  of  the  assump- 
tion, and  the  reality  of  the  existence  of  a  primitive  form, 
at  least  in  a  sense  not  very  different  from  the  usual  sense 
of  the  expression."  He  then  proceeds  to  relate  that  he 
sought  a  ground  for  such  an  opinion,  independent  of  the 
doctrine  of  atoms,  which  he,  in  common  with  a  great 
number  of  philosophers  of  that  time  in  his  own  country, 
was  disposed  to  reject,  inclining  to  believe  that  the  pro- 
perties of  bodies  were  determined  by  forces  which  acted 
in  them,  and  not  by  molecules  of  which  they  were  com- 
posed. He  adds,  that  in  pursuing  this  train  of  thought, 

*  Acad.  Berlin.  1816.  p.  307. 


SPECULATIONS  ON  THE  SYMMETRY  OF  CRYSTALS.       441 

he  found,  "  that  out  of  his  primitive  forms  there  was  gra- 
dually unfolded  to  his  hands  that  which  really  governs 
them,  and  is  not  affected  by  their  casual  fluctuations ; 
namely,  the  fundamental  relations  of  their  Dimensions," 
or  as*we  now  may  call  them,  Axes  of  Symmetry.  With 
reference  to  these  axes,  he  found,  as  he  goes  on  to  say, 
that  "a  multiplicity  of  internal  oppositions,  necessarily 
and  mutually  interdependent,  are  developed  in  the  crys- 
talline mass,  each  relation  having  its  own  polarity;  so 
that  the  crystalline  character  is  co-extensive  with  these 
polarities."  The  character  of  these  polarities,  whether 
manifested  in  crystalline  faces,  cleavage,  or  any  other 
incidents  of  crystallization,  is  necessarily  displayed  in  the 
degree  and  kind  of  symmetry  which  the  crystal  possesses: 
and  thus  this  symmetry,  in  all  our  speculations  concern- 
ing the  structure  of  crystals,  necessarily  takes  the  place 
of  that  enumeration  of  primitive  forms  which  were  re- 
jected as  inconsistent  with  observed  facts,  and  destitute 
of  sound  scientific  principle. 

I  may  just  notice  here  what  I  have  stated  in  the  His- 
tory of  Mineralogy*,  that  the  distinction  of  systems  of 
crystallization,  as  introduced  by  Weiss  and  Mohs,  was 
strikingly  confirmed  by  Sir  David  Brewster's  discoveries 
respecting  the  optical  properties  of  minerals.  The  splen- 
did phenomena  which  were  produced  by  passing  polarized 
light  through  crystals,  were  found  to  vary  according  as 
the  crystals  were  of  the  rhombohedral,  square  pyramidal, 
oblong  prismatic,  or  tessular  system.  The  optical  exactly 
corresponded  with  the  geometrical  symmetry.  In  the 
two  former  systems  were  crystals  uniaxal  in  respect  of 
their  optical  properties ;  the  oblong  prismatic  was  biaxal; 
while  in  the  tessular,  the  want  of  a  predominant  axis  pre- 
vented the  phenomena  here  spoken  of  from  occurring  at 
all.  The  optical  experiments  must  have  led  to  a  classifi- 

*  Hist.  Tnd.  Sci.,  iii.  217- 


442  PHILOSOPHY   OF  MORPHOLOGY. 

cation  of  crystals  into  the  above  systems  or  something 
nearly  equivalent,  even  had  they  not  been  already  so 
arranged  by  attention  to  their  forms. 

4.  While  in  Germany  Weiss  and  Mohs  with  their 
disciples,  were  gradually  rejecting  what  was  superfluous 
in  the  previous  crystallographical  hypotheses,  philosophers 
in  England  were  also  trying  to  represent  to  themselves 
the  constitution  of  crystals  in  a  manner  which  should  be 
free  from  the  obviously  arbitrary  and  untenable  fictions 
of  the  Haiiyian  school.  These  attempts,  howrever,  were 
not  crowned  with  much  success.  One  mode  of  repre- 
senting the  structure  of  crystals  which  suggested  itself, 
was  to  reject  the  polyhedral  forms  which  Haiiy  gave  to 
his  integrant  molecules,  and  to  conceive  the  elements  of 
crystals  as  spheres,  the  properties  of  the  crystal  being 
determined  not  by  the  surfaces,  but  by  the  position  of 
the  elements.  Tnis  was  done  by  Wollaston,  in  the  Phi- 
losophical Transactions  for  1813.  He  applied  this  view  to 
the  tessular  system,  in  which,  indeed,  the  application  is 
not  difficult ;  and  he  showed  that  octahedral  and  tetrahe- 
dral  figures  may  be  deduced  from  symmetrical  arrange- 
ments of  equal  spherules.  But  though  in  doing  this,  he 
manifested  a  perception  of  the  conditions  of  the  problem, 
he  appeared  to  lose  his  hold  on  the  real  question  when  he 
tried  to  pass  on  to  other  systems  of  crystallization.  For 
he  accounted  for  the  rhombohedral  system  by  supposing 
the  spheres  changed  into  spheroids.  Such  a  procedure 
involved  him  in  a  gratuitous  and  useless  hypothesis :  for 
to  what  purpose  do  we  introduce  the  arrangement  of 
atoms  (instead  of  their  figure,)  as  a  mode  of  explaining 
the  symmetry  of  the  crystallization,  when  at  the  next 
step  we  ascribe  to  the  atom,  by  an  arbitrary  fiction,  a 
symmetry  of  figure  of  the  same  kind  as  that  which  we 
have  to  explain  ?  It  is  just  as  easy,  and  as  allowable,  to 
assume  an  elementary  rhombohedron,  as  to  assume  ele- 


SPECULATIONS  ON  THE  SYMMETRY  OF  CRYSTALS.       443 

mentary   spheroids,    of    which   the   rhombohedrons   are 
constructed. 

5.  Many  hypotheses  of  the  same  kind  might  be 
adduced,  devised  both  by  mineralogists  and  chemists. 
But  almost  all  such  speculations  have  been  pursued  with 
a  most  surprising  neglect  of  the  principle  which  obviously 
is  the  only  sound  basis  on  which  they  can  proceed. 
The  principle  is  this : — that  all  hypotheses  concerning  the 
arrangement  of  the  elementary  atoms  of  bodies  in  space 
must  be  constructed  with  reference  to  the  general  facts  of 
crystallization.  The  truth  and  importance  of  this  prin. 
ciple  can  admit  of  no  doubt.  For  if  we  make  any 
hypothesis  concerning  the  mode  ef  connexion  of  the 
elementary  particles  of  bodies,  this  must  be  done  with 
the  view  of  representing  to  ourselves  the  forces  which 
connect  them,  and  the  results  of  these  forces  as  mani- 
fested in  the  properties  of  the  bodies.  Now  the  forces 
which  connect  the  particles  of  bodies  so  as  to  make 
them  crystalline,  are  manifestly  chemical  forces.  It  is 
only  definite  chemical  compounds  which  crystallize ;  and 
in  crystals  the  force  of  cohesion  by  which  the  particles 
are  held  together  cannot  in  any  way  be  distinguished  or 
separated  from  the  chemical  force  by  which  their  elements 
are  combined.  The  elements  are  understood  to  be  com- 
bined, precisely  because  tne  result  is  a  definite,  apparently 
homogeneous  substance.  The  properties  of  the  com- 
pound bodies  depend  upon  the  elements  and  their  mode 
of  combination ;  for,  in  fact,  these  include  everything  on 
which  they  can  depend.  There  are  no  other  circum- 
stances than  these  which  can  affect  the  properties  of  a 
body.  Therefore  all  those  properties  which  have  refer- 
ence to  space,  namely,  the  crystalline  properties,  cannot 
depend  upon  anything  else  than  the  arrangement  of  the 
elementary  molecules  in  space.  These  properties  are 
the  facts  which  any  hypothesis  of  the  arrangement  of 


444  PHILOSOPHY  OF  MORPHOLOGY. 

molecules  must  explain,  or  at  least  render  conceivable ; 
and  all  such  hypotheses,  all  constructions  of  bodies  by 
supposed  arrangements  of  molecules,  can  have  no  other 
philosophical  object  than  to  account  for  facts  of  this 
kind.  If  they  do  not  do  this,  they  are  mere  arbitrary 
geometrical  fictions,  which  cannot  be  in  any  degree  con- 
firmed or  authorized  by  an  examination  of  nature,  and 
are  therefore  not  deserving  of  any  regard. 

6.  Those  philosophers  who  have  endeavoured  to  repre- 
sent the  mode  in  which  bodies  are  constructed  by  the 
combination  of  their  chemical  atoms,  have  often  under- 
taken to  show,  not  only  that  the  atoms  are  combined,  but 
also  in  what  positions  and  configurations  they  are  com- 
bined. And  it  is  truly  remarkable,  as  I  have  already 
said,  that  they  have  done  this,  almost  in  every  instance, 
without  any  consideration  of  the  crystalline  character  of 
the  resulting  combinations  ;  from  which  alone  we  receive 
any  light  as  to  the  relation  of  their  elements  in  space. 
Thus  Dr.  Dalton,  in  his  Elements  of  Chemistry,  in  which 
he  gave  to  the  world  the  Atomic  Theory  as  a  representa- 
tion of  the  doctrine  of  definite  and  multiple  proportions, 
also  published  a  large  collection  of  diagrams,  exhibiting 
what  he  conceived  to  be  the  configuration  of  the  atoms 
in  a  great  number  of  the  most  common  combinations  of 
chemical  elements.  Now  these  hypothetical  diagrams 
do  not  in  any  way  correspond,  as  to  the  nature  of  their 
symmetry,  with  the  compounds,  as  we  find  them  display- 
ing their  symmetry  when  they  occur  crystallized.  Car- 
bonate of  lime  has  in  reality  a  triangular  symmetry,  since 
it  belongs  to  the  rhombohedral  system;  Dr.  Dalton's 
carbonate  of  lime  would  be  an  oblique  rhombic  prism  or 
pyramid.  Sulphate  of  baryta  is  really  two-and-two 
membered ;  Dr.  Dalton's  diagram  makes  it  two-and-one 
membered.  Alum  is  really  octahedral  or  tessular ;  but 
according  to  the  diagram  it  could  not  be  so,  since  the 


SPECULATIONS  ON  THE  SYMMETRY  OF  CRYSTALS.       445 

two  ends  of  the  atom  are  not  symmetrical.  And  the 
same  want  of  correspondence  between  the  facts  and  the 
hypothesis  runs  through  the  whole  system.  It  need  not 
surprise  us  that  the  theoretical  arrangement  of  atoms 
does  not  explain  the  facts  of  crystallization ;  for  to  pro- 
duce such  an  explanation  would  be  a  second  step  in 
science  quite  as  great  as  the  first,  the  discovery  of  the 
atomic  theory  in  its  chemical  sense.  But  we  may  allow 
ourselves  to  be  surprised  that  an  utter  discrepance  be- 
tween all  the  facts  of  crystallization  and  the  figures 
assumed  in  the  theory,  did  not  suggest  any  doubt  as  to 
the  soundness  of  the  mode  of  philosophizing  by  which 
this  part  of  the  theory  was  constructed. 

7.  Some  little  accordance  between  the  hypothetical 
arrangements  of  chemical  atoms  and  the  facts  of  crystal- 
lization, does  appear  to  have  been  arrived  at  by  some  of 
the  theorists  to  whom  we  here  refer,  although  by  no 
means  enough  to  show  a  due  conviction  of  the  importance 
of  the  principle  stated  above.  Thus  Wollaston,  in  the 
Essay  above  noticed,  after  showing  that  a  symmetrical 
arrangement  of  equal  spherules  would  give  rise  to  octa- 
hedral and  other  tessular  figures,  remarks,  very  properly, 
that  the  metals,  which  are  simple  bodies,  crystallize  in 
such  forms.  M.  Ampere*  also,  in  1814,  published  a 
brief  account  of  an  hypothesis  of  a  somewhat  similar 
nature,  and  stated  himself  to  have  developed  this  specu- 
lation in  a  Memoir  which  has  not  yet,  so  far  as  I  am 
aware,  been  published.  In  this  notice  he  conceives  bodies 
to  be  compounded  of  molecules,  which,  arranged  in  a  poly- 
hedral form,  constitute  particles.  These  representative 
forms  of  the  particles  depend  on  chemical  laws.  Thus 
the  particles  of  oxygen,  of  hydrogen,  and  of  azote,  are 
composed  each  of  four  molecules.  Hence  it  is  collected 
that  the  particles  of  nitrous  gas  are  composed  of  two 

*  Ann.de  Chimie,  torn.  xc.  p.  43. 


446  PHILOSOPHY  OF  MORPHOLOGY. 

molecules  of  oxygen  and  two  of  azote ;  and  similar  con- 
clusions are  drawn  respecting  other  substances.  These 
conclusions,  though  expressed  by  means  of  the  polyhe- 
drons thus  introduced,  are  supported  by  chemical,  rather 
than  by  crystallographical  comparisons.  The  author  does, 
indeed,  appeal  to  the  crystallization  of  sal  ammoniac  as 
an  argument*;  but  as  all  the  forms  which  he  introduces 
appear  to  belong  to  the  tessular  system  of  crystallization, 
there  is,  in  his  reasonings,  nothing  distinctive;  and 
therefore  nothing,  crystallographically  speaking,  of  any 
weight  on  the  side  of  this  theory. 

8.  Any  hypothesis  which  should  introduce  any  prin- 
ciple of  chemical  order  among  the  actual  forms  of  mine- 
rals, would  well  deserve  attention.  At  first  sight,  nothing 
can  appear  more  anomalous  than  the  forms  which  occur. 
We  have,  indeed,  one  broad  fact,  which  has  an  encou- 
raging aspect,  the  tessular  forms  in  which  the  pure  metals 
crystallize.  The  highest  degree  of  chemical  and  of  geo- 
metrical simplicity  coincide :  irregularity  disappears  pre- 
cisely where  it  is  excluded  by  the  consideration  above 
stated,  that  the  symmetry  of  chemical  composition  must 
determine  the  symmetry  of  crystalline  form. 

But  if  we  go  on  to  any  other  class  of  crystalline 
forms,  we  soon  find  ourselves  lost  in  our  attempts  to 
follow  any  thread  of  order.  We  have  indeed  many  large 
groups  connected  by  obvious  analogies ;  as  the  rhombo- 
hedral  carbonates  of  lime,  magnesia,  iron,  manganese  ;— 
the  prismatic  carbonates  and  sulphates  of  lime,  baryta, 
strontia,  lead.  But  even  in  these,  we  cannot  form  any 
plausible  hypothesis  of  the  arrangement  of  the  elements ; 
and  in  other  cases  to  which  we  naturally  turn,  we  can 
find  nothing  but  confusion.  For  instance,  if  we  examine 
the  oxides  of  metals : — those  of  iron  are  rhombohedral 
and  tessular ;  those  of  copper,  tessular ;  those  of  tin,  of 

*  Ann.  de  Chirme,  torn.  xc.  p.  83. 


SPECULATIONS  ON  THE  SYMMETRY  OF  CRYSTALS.      447 

titanium,  of  manganese,  square  pyramidal;  those  of 
antimony,  prismatic  ;  and  we  have  other  forms  for  other 
substances. 

It  may  be  added,  that  if  we  take  account  of  the 
optical  properties  which,  as  we  have  already  stated,  have 
constant  relations  to  the  crystalline  forms,  the  confusion 
is  still  further  increased ;  for  the  optical  dimensions  vary 
in  amount,  though  not  in  symmetry,  where  chemistry  can 
trace  no  difference  of  composition. 

9.  We  will  not  quit  the  subject,  however,  without 
noticing  the  much  more  promising  aspect  which  it 
has  assumed  by  the  detection  of  such  groups  as  are 
referred  to  in  the  last  article ;  or  in  other  words,  by 
Mitscherlich's  discovery  of  Isomorphism.  According  to 
that  discovery,  there  are  various  elements  which  may 
take  the  place  of  each  other  in  crystalline  bodies,  either 
without  any  alteration  of  the  crystalline  form,  or  at  most 
with  only  a  slight  alteration  of  its  dimensions.  Such  a 
group  of  elements  we  have  in  the  earths  lime  and  mag- 
nesia, the  protoxides  of  iron  and  manganese :  for  the  car- 
bonates of  all  these  bases  occur  crystallized  in  forms  of 
the  rhombohedral  system,  the  characteristic  angle  being 
nearly  the  same  in  all.  Now  lime  and  magnesia,  by  the 
discoveries  of  modern  chemistry,  are  really  oxides  of 
metals ;  and  therefore  all  these  carbonates  have  a  similar 
chemical  constitution,  while  they  have  also  a  similar 
crystalline  form.  Whether  or  no  we  can  devise  any 
arrangement  of  molecules  by  which  this  connexion  of 
the  chemical  and  the  geometrical  property  can  be  repre- 
sented, we  cannot  help  considering  the  connexion  as  an 
extremely  important  fact  in  the  constitution  of  bodies ; 
and  such  facts  are  more  likely  than  any  other  to  give  us 
some  intelligible  view  of  the  relations  of  the  ultimate 
parts  of  bodies.  The  same  may  be  said  of  all  the  other 


448  PHILOSOPHY  OF   MORPHOLOGY. 

isomorphous  or  plesiomorphous  groups*.  For  instance, 
we  have  a  number  of  minerals  which  belong  to  the  same 
system  of  crystallization,  but  in  which  the  chemical  com- 
position appears  at  first  sight  to  be  very  various :  namely, 
spinelle,  pleonaste,  gahnite,  franklinite,  chromic  iron 
oxide,  magnetic  iron  oxide :  but  Abich  has  shown  that 
all  these  may  be  reduced  to  a  common  chemical  formula ; 
— they  are  bioxides  of  one  set  of  bases,  combined  with 
trioxides  of  another  set.  Perhaps  some  mathematician 
may  be  able  to  devise  some  geometrical  arrangement  of 
such  a  group  of  elements  which  may  possess  the  properties 
of  the  tessular  system.  Hypothetical  arrangements  of 
atoms,  thus  expressing  both  the  chemical  and  the  crys- 
talline symmetry  which  we  know  to  belong  to  the  sub- 
stance, would  be  valuable  steps  in  analytical  science ;  and 
when  they  had  been  duly  verified,  the  hypotheses  might 
easily  be  divested  of  their  atomic  character. 

Thus,  as  we  have  already  said,  mineralogy,  understood 
in  its  wider  sense,  as  the  counterpart  of  chemistry,  has 
for  one  of  its  main  objects  to  discover  those  relations  of 
the  elements  of  bodies  which  have  reference  to  space. 
In  this  research,  the  foundation  of  all  sound  speculation 
is  the  kind  and  degree  of  symmetry  of  form  which  we 
find  in  definite  chemical  compounds:  and  the  problem 
at  present  before  the  inquirer  is,  to  devise  such  arrange- 
ments of  molecules  as  shall  answer  the  conditions  alike 
of  chemistry  and  of  crystallography. 

We  now  proceed  to  the  Classificatory  Sciences,  of 
which  mineralogy  is  one,  though  hitherto  by  far  the  least 
successful. 

*  See  Hist.  Ind.  8ci.9  Hi.  222. 


449 


BOOK  VIII. 


THE  PHILOSOPHY  OF  THE  CLASSIFICATORY 
SCIENCES. 


CHAPTER  I. 

THE  IDEA  OF  LIKENESS  AS  GOVERNING  THE 
USE  OF  COMMON  NAMES. 

1.  Object  of  the  Chapter. — Not  only  the  Classificatory 
Sciences,  but  the  application  of  names  to  things  in  the 
rudest  and  most  unscientific  manner,  depends  upon  our 
apprehending  them  as  like  each  other.     We  must  there- 
fore endeavour  to  trace  the  influence  and  operation  of 
the  Idea  of  Likeness  in  the  common  use  of  language, 
before  we  speak  of  the  conditions  under  which  it  acquires 
its  utmost  exactness  and  efficacy. 

It  will  be  my  object  to  show  in  this,  as  in  previous 
cases,  that  the  impressions  of  sense  are  apprehended  by 
acts  of  the  mind ;  and  that  these  mental  acts  necessarily 
imply  certain  relations  which  may  be  made  the  subjects 
of  speculative  reasoning.  We  shall  have,  if  we  can,  to 
seize  and  bring  into  clear  view  the  principles  which  the 
relation  of  like  and  unlike  involves,  and  the  mode  in 
which  these  principles  have  been  developed. 

2.  Unity  of  the  Individual. — But  before  we  can  attend 
to  several  things  as  like  or  unlike,  we  must  be  able  to 
apprehend  each  of  these  by  itself  as  one  thing.     It  may  at 
first  sight  perhaps  appear  that  this  apprehension  results 
immediately  from  the  impressions  on  our  senses,  without 

VOL.  i.  2  G 


450      PHILOSOPHY  OF  THE  CLASSIFICATORY  SCIENCES. 

any  act  of  our  thoughts.  A  very  little  attention,  how- 
ever, enables  us  to  see  that  thus  to  single  out  special 
objects  requires  a  mental  operation  as  well  as  a  sensation. 
How,  for  example,  without  an  exertion  of  mental  activity, 
can  we  see  one  tree,  in  a  forest  where  there  are  many  ?  We 
have,  spread  before  us,  a  collection  of  colours  and  forms, 
green  and  brown,  dark  and  light,  irregular  and  straight : 
this  is  all  that  sensation  gives  or  can  give.  But  we  asso- 
ciate one  brown  trunk  with  one  portion  of  the  green  mass, 
excluding  the  rest,  although  the  neighbouring  leaves  are 
both  nearer  in  contiguity  and  more  similar  in  appearance 
than  is  the  stem.  We  thus  have  before  us  one  tree ;  but 
this  unity  is  given  by  the  mind  itself.  We  see  the  green 
and  the  brown,  but  we  must  make  the  tree  before  we  can 
see  it. 

That  this  composition  of  our  sensations  so  as  to  form 
one  thing  implies  an  act  of  our  own,  will  perhaps  be  more 
readily  allowed,  if  we  once  more  turn  our  attention  to 
the  manner  in  which  we  sometimes  attempt  to  imitate 
and  record  the  objects  of  sight,  by  drawing.  When  we  do 
this,  as  we  have  already  observed,  we  mark  this  unity  of  each 
object,  by  drawing  a  line  to  separate  the  parts  which  we 
include  from  those  which  we  exclude ; — an  Outline.  This 
line  corresponds  to  nothing  which  we  see ;  the  beginner 
in  drawing  has  great  difficulty  in  discerning  it ;  he  has  in 
fact  to  make  it.  It  is,  as  has  been  said  by  a  painter  of 
our  own  time*,  a  fiction :  but  it  is  a  fiction  employed  to 
mark  a  real  act  of  the  mind ;  to  designate  the  singleness 
of  the  object  in  our  conception.  As  we  have  said  else- 
where, we  see  lines,  but  especially  outlines,  by  mentally 
drawing  them  ourselves. 

The  same  act  of  conception  which  the  outline  thus 
represents  and  commemorates  in  visible  objects, — the  same 
combination  of  sensible  impressions  into  a  unit, — is  exer- 

*  PHILLIPS  on  Painting)— Design. 


THE   IDEA  OF  LIKENESS.  451 

cised  also  with  regard  to  the  objects  of  all  our  senses :  and 
the  singleness  thus  given  to  each  object,  is  a  necessary 
preliminary  to  its  being  named  or  represented  in  any 
other  way. 

But  it  may  be  said,  Is  it  then  by  an  arbitrary  act  of 
our  own  that  we  put  together  the  branches  of  the  same 
tree,  or  the  limbs  of  the  same  animal  ?  Have  we  equally 
the  power  and  the  right  to  make  the  branch  of  the  fir  a 
part  of  the  neighbouring  oak?  Can  we  include  in  the 
outline  of  a  man  any  object  with  which  he  happens  to  be 
in  contact? 

Such  suppositions  are  manifestly  absurd.  And  the 
answer  is,  that  though  we  give  unity  to  objects  by  an 
act  of  thought,  it  is  not  by  an  arbitrary  act ;  but  by  a 
process  subject  to  certain  conditions :  to  conditions  which 
exclude  such  incongruous  combinations  as  have  just  been 
spoken  of. 

What  are  these  conditions  which  regulate  our  appre- 
hension  of  an  object  as  one  ?  which  determine  what  por- 
tion of  our  impressions  does,  and  what  portion  does  not 
belong  to  the  same  thing  ? 

2.  Condition  of  Unity. — I  reply,  that  the  primary  and 
fundamental  condition  is,  that  we  must  be  able  to  make 
intelligible  assertions  respecting  the  object,  and  to  enter- 
tain that  belief  of  which  assertions  are  the  exposition.  A 
tree  grows,  sheds  its  leaves  in  autumn,  and  buds  again  in 
the  spring,  waves  in  the  wind,  or  falls  before  the  storm. 
And  to  the  tree  belong  all  those  parts  which  must  be 
included  in  order  that  such  declarations,  and  the  thoughts 
which  they  convey,  shall  have  a  coherent  and  permanent 
meaning.  Those  are  its  branches  which  wave  and  fall  with 
its  trunk ;  those  are  its  leaves  which  grow  on  its  branches. 
The  permanent  connexions  which  we  observe, — perma- 
nent, among  unconnected  changes  which  affect  the  sur- 
rounding appearances, — are  what  we  bind  together  as 

2  G  2 


452       PHILOSOPHY  OF  THE  CLASSIFICATORY  SCIENCES. 

belonging  to  one  object.  This  permanence  is  the  condi- 
tion of  our  conceiving  the  object  as  one.  The  connected 
changes  may  always  be  described  by  means  of  assertions ; 
and  the  connexion  is  seen  in  the  identity  of  the  subject  of 
successive  predications;  in  the  possibility  of  applying 
many  verbs  to  one  substantive.  We  may  therefore  express 
the  condition  of  the  unity  of  an  object  to  be  this :  that 
assertions  concerning  the  object  shall  be  possible :  or  rather 
we  should  say,  that  the  acts  of  belief  which  such  assertions 
enunciate  shall  be  possible. 

It  may  seem  to  be  superfluous  to  put  in  a  form  so 
abstract  and  remote,  the  grounds  of  a  process  apparently 
so  simple  as  our  conceiving  an  object  to  be  one.  But 
the  same  condition  to  which  we  have  thus  been  led,  as 
the  essential  principle  of  the  unity  of  objects,  namely, 
that  propositions  shall  be  possible,  will  repeatedly  occur 
in  the  present  chapter ;  and  it  may  serve  to  illustrate  our 
views,  to  show  that  this  condition  pervades  even  the 
simplest  cases. 

4.  Kinds. — The  mental  synthesis  of  which  we  have 
thus  spoken,  gives  us  our  knowledge  of  individual  things ; 
it  enables  me  to  apprehend  that  particular  tree  or  man 
which  I  now  see,  or,  by  the  help  of  memory,  the  tree  or 
the  man  I  saw  yesterday.  But  the  knowledge  with 
which  we  have  mainly  here  to  do  is  not  a  knowledge  of 
individuals  but  of  kinds ;  of  such  classes  as  are  indicated 
by  common  names.  We  have  to  make  assertions  con- 
cerning a  tree  or  a  man  in  general,  without  regarding 
what  is  peculiar  to  this  man  or  that  tree. 

Now  it  is  clear  that  certain  individual  objects  are  all 
called  man,  or  all  called  tree,  in  virtue  of  some  resemblance 
which  they  have.  If  we  had  not  the  power  of  perceiving 
in  the  appearances  around  us,  likeness  and  unlikeness, 
we  could  not  consider  objects  as  distributed  into  kinds  at 
all.  The  impressions  of  sense  would  throng  upon  us,  but 


THE  IDEA  OF  LIKENESS.  453 

being  uncompared  with  each  other,  they  would  flow  away 
like  the  waves  of  the  sea,  and  each  vanish  from  our  con- 
templation when  the  sensation  faded.  That  we  do  appre- 
hend surrounding  objects  as  belonging  to  permanent  kinds, 
as  being  men  and  horses,  oaks  and  roses,  arises  from  our 
having  the  idea  of  likeness,  and  from  our  applying  it 
habitually,  and  so  far  as  such  a  classification  requires. 

Not  only  can  we  employ  the  idea  of  likeness  in  this 
manner,  but  we  apply  it  incessantly  and  universally  to 
the  whole  mass  and  train  of  our  sensations.  For  we  have 
no  external  sensations  to  which  we  cannot  apply  some 
language  or  other,  and  all  language  necessarily  implies 
recognition  of  resemblances.  We  cannot  call  an  object 
green  or  round  without  comparing  in  our  thoughts  its 
colour  or  its  shape,  with  a  shape  and  a  colour  seen  in 
other  objects.  All  our  sensations,  therefore,  without  any 
exception  of  kind  or  time,  are  subject  to  this  constant 
process  of  classification ;  and  the  idea  of  likeness  is  per- 
petually operating  to  distribute  them  into  kinds,  at  least 
so  far  as  the  use  of  language  requires. 

We  come  then  again  to  the  question,  Upon  what 
principle,  under  what  conditions,  is  the  idea  of  likeness 
thus  operative  ?  What  are  the  limits  of  the  classes  thus 
formed  ?  Where  does  that  similarity  end,  which  induces 
and  entitles  us  to  call  a  thing  a  tree  ?  What  universal 
rule  is  there  for  the  application  of  common  names,  so 
that  we  may  not  apply  them  wrongly  ? 

5.  Not  made  ty  Definitions. — Perhaps  some  one  might 
expect  in  answer  to  these  inquiries  a  definition  or  a  series 
of  definitions ; — might  imagine  that  some  description  of  a 
tree  might  be  given  which  might  show  when  the  term 
was  applicable  and  when  it  was  not ;  and  that  we  might 
construct  a  body  of  rules  to  which  such  descriptions  must 
conform.  But  on  consideration  it  will  be  clear  that  the 
real  solution  of  our  difficulty  cannot  be  obtained  in  such 


454         PHILOSOPHY  OP  THE  CLASSIFICATORY  SCIENCES. 

a  manner.  For  first;  such  descriptions  must  be  given  in 
words,  and  therefore  suppose  that  we  have  already  satisfied 
ourselves  how  words  are  to  be  used.  If  we  define  a 
tree  to  be  a  living  thing  without  the  power  of  voluntary 
motion,  we  shall  be  called  upon  to  define  a  living  thing ; 
and  it  is  manifest  that  this  renewal  of  the  demand  for 
definition  might  be  repeated  indefinitely ;  and,  therefore, 
we  cannot  in  this  way  come  to  a  final  principle.  And  in 
the  next  place,  most  of  those  who  use  language,  even  with 
great  precision  and  consistency,  would  find  it  difficult  or 
impossible  to  give  good  definitions  even  of  a  few  of  the 
general  names  which  they  use ;  and  therefore  their  prac- 
tice cannot  be  regulated  by  any  tacit  reference  to  such  de- 
finitions. That  definitions  of  terms  are  of  great  use  and 
importance  in  their  right  place,  we  shall  soon  see ;  but 
their  place  is  not  to  regulate  the  use  of  common  language. 

What  then,  once  more,  is  this  regulative  principle  ? 
What  rules  do  men  follow  in  the  use  of  words,  so  as 
commonly  to  avoid  confusion  and  ambiguity?  How  do 
they  come  to  understand  each  other  so  well  as  they 
ordinarily  do,  respecting  the  limits  of  classes  never  de- 
fined, and  which  they  cannot  define?  What  is  the 
common  convention,  or  condition  to  which  they  conform? 

6.  Condition  of  the  Use  of  Terms. — To  this  we  reply, 
that  the  condition  which  regulates  the  use  of  language, 
is  that  it  shall  be  capable  of  being  used  ; — that  is,  that 
general  assertions  shall  be  possible.  The  term  tree  is 
applicable  as  far  as  it  is  useful  in  expressing  our  know- 
ledge concerning  trees : — thus  we  know  that  trees  are 
fixed  in  the  ground,  have  a  solid  stem,  branches,  leaves, 
and  many  other  properties.  With  regard  to  all  the  objects 
which  surround  us,  we  have  an  immense  store  of  know- 
ledge of  such  properties,  and  we  employ  the  names  of  the 
objects  in  such  a  manner  as  enables  us  to  express  these 
properties. 


THE  IDEA  OF  LIKENESS.  455 

But  the  connexion  of  such  properties  is  variable  and  in- 
definite. Some  properties  are  constantly  combined,  others 
occasionally  only.  The  leaves  of  different  oaks  resemble 
each  other,  the  branches  resemble  far  less,  and  may  differ 
very  widely.  The  term  oak  does  not  enable  us  to  say  that 
all  oaks  have  straight  branches  or  all  crooked.  Terms  can 
only  express  properties  as  far  as  they  are  constant.  Not 
only,  therefore,  the  accumulation  of  a  vast  mass  of  know- 
ledge of  the  properties  and  attributes  of  objects,  but  also 
an  observation  of  the  habitual  connexion  of  such  properties 
is  needed,  to  direct  us  to  the  consistent  application  of 
terms : — to  enable  us  to  apply  them  so  as  to  express 
truths.  But  here  again  we  are  largely  provided  with  the 
requisite  knowledge  and  observation  by  the  common 
course  of  our  existence.  The  unintermitting  stream  of 
experience  supplies  us  with  an  incalculable  amount  of 
such  observed  connexions.  All  men  have. observed  that 
the  associations  of  the  same  form  of  leaves  are  more  con- 
stant than  of  the  same  form  of  branches ; — that  though 
persons  walk  in  different  attitudes  none  go  on  all  fours  ; 
and  thus  the  term  oak  is  so  applied  as  to  include  those 
cases  in  which  the  leaves  are  alike  in  form  though  the 
branches  be  unlike ;  and  though  we  should  refuse  to 
apply  the  term  man  to  a  class  of  creatures  which  habi- 
tually and  without  compulsion  used  four  legs,  we  make  no 
scruple  of  affixing  it  to  persons  of  very  different  figures. 
The  whole  of  human  experience  being  composed  of  such 
observed  connexions,  we  have  thus  materials  even  for 
the  immense  multiplicity  of  names  which  human  language 
contains ;  all  which  names  are,  as  we  have  said,  regulated 
in  their  application  by  the  condition  of  expressing  such 
experience. 

Thus  amid  the  countless  combinations  of  properties 
and  divisions  of  classes  which  the  structure  of  language 
implies,  scarcely  any  are  arbitrary  or  capricious.  A  word 


456        PHILOSOPHY  OF  THE  CLASSIFICATORY  SCIENCES. 

which  expressed  a  mere  wanton  collection  of  unconnected 
attributes  could  hardly  be  called  a  word ;  for  of  such  a 
collection  of  properties  no  truth  could  be  asserted,  and 
the  word  would  disappear,  for  want  of  some  occasion  on 
which  it  could  be  used.  Though  much  of  the  fabric  of 
language  appears,  not  unnaturally,  fantastical  and  purely 
conventional,  it  is  in  fact  otherwise.  The  associations 
and  distinctions  of  phraseology  are  not  more  fanciful  than 
is  requisite  to  make  them  correspond  to  the  apparent 
caprices  of  nature  or  of  thought ;  and  though  much  in 
language  may  be  called  conventional,  the  conventions 
exist  for  the  sake  of  expressing  some  truth  or  opinion, 
and  not  for  their  own  sake.  The  principle,  that  the  con- 
dition of  the  use  of  terms  is  the  possibility  of  general,  intelli- 
gible, consistent  assertions,  is  true  in  the  most  complete 
and  extensive  sense. 

7.  Terms  may  have  different  Uses. — The  terms  with 
which  we  are  here  most  concerned  are  names  of  classes 
of  natural  objects ;  and  when  we  say  that  the  principle 
and  the  limit  of  such  names  are  their  use  in  expressing 
propositions  concerning  the  classes,  it  is  clear  that  much 
will  depend  on  the  kind  of  propositions  which  we  mainly 
have  to  express:  and  that  the  same  name  may  have 
different  limits,  according  to  the  purpose  we  have  in  view. 
For  example,  is  the  whale  properly  included  in  the 
general  term  fish  f  When  men  are  concerned  in  catching 
marine  animals,  the  main  features  of  the  process  are  the 
same  however  the  animals  may  differ ;  hence  whales  are 
classed  with  fishes,  and  we  speak  of  the  whale-fishery. 
But  if  we  look  at  the  analogies  of  organization,  we  find 
that,  according  to  these,  the  whale  is  clearly  not  a  fish,  but 
a  beast,  (confining  this  term,  for  the  sake  of  distinctness, 
to  suckling  beasts  or  mammals).  In  Natural  History,  there- 
fore, the  whale  is  not  included  among  fish.  The  indefi- 
nite and  miscellaneous  propositions  which  language  is 


THE  IDEA  OF  LIKENESS.  457 

employed  to  enunciate  in  the  course  of  common  practical 
life,  are  replaced  by  a  more  coherent  and  systematic 
collection  of  properties,  when  we  come  to  aim  at  scientific 
knowledge.  But  we  shall  hereafter  consider  the  principle 
of  the  classifications  of  Natural  History;  our  present 
subject  is  the  application  of  the  Idea  of  Likeness  in 
common  practice  and  common  language. 

8.  Gradation  of  Kinds. — Common  names,  then,  in- 
clude many  individuals  associated  in  virtue  of  resem- 
blances, and  of  permanently  connected  properties ;  and 
such  names  are  applicable  as  far  as  they  serve  to  express 
such  properties.  These  collections  of  individuals  are 
termed  kinds,  sorts,  classes. 

But  this  association  of  particulars  is  capable  of  degrees. 
As  individuals  by  their  resemblances  form  kinds,  so  kinds 
of  things,  though  different,  may  resemble  each  other  so  as 
to  be  again  associated  in  a  higher  class ;  and  there  may 
be  several  successive  steps  of  such  classification.  Man, 
horse,  tree,  stone,  are  each  a  name  of  a  kind ;  but  animal 
includes  the  two  first  and  excludes  the  others;  living 
thing  is  a  term  which  includes  animal  and  tree  but  not 
stone ;  body  includes  all  the  four.  And  such  a  subordi- 
nation of  kinds  may  be  traced  very  widely  in  the  arrange- 
ments of  language. 

The  condition  of  the  use  of  the  wider  is  the  same  as 
that  of  the  narrower  names  of  classes ; — they  are  good  as 
far  as  they  serve  to  express  true  propositions.  In  com- 
mon language,  though  such  an  order  of  generality  may  in 
a  variety  of  instances  be  easily  discerned,  it  is  not  sys- 
tematically and  extensively  referred  to ;  but  this  subordi- 
nation and  graduated  comprehensiveness  is  the  essence  of 
the  methods  and  nomenclatures  of  Natural  History,  as  we 
shall  soon  have  to  show. 

But  such  subordination  is  not  without  its  use,  even  in 
common  cases,  and  when  it  is  expressed  in  the  terms  of 


458        PHILOSOPHY  OF  THE  CLASSIFICATORY  SCIENCES. 

common  language.  Thus  organized  body  is  a  term  which 
includes  plants  and  animals ;  animal  includes  beasts,  birds, 
fishes ;  beast  includes  horses  and  dogs ;  dogs,  again,  are 
greyhounds,  spaniels,  terriers. 

9.  Characters  of  Kinds. — Now  when  we  have  such  a 
series  of  names  and  classes,  we  find  that  we  take  for 
granted  irresistibly  that  each  class  has  some  character 
which  distinguishes  it  from  other  classes  included  in  the 
superior  division.  We  ask  what  kind  of  beast  a  dog  is ; 
what  kind  of  animal  a  beast  is ;  and  we  assume  that  such 
questions  admit  of  answer; — that  each  kind  has  some 
mark  or  marks  by  which  it  may  be  described.  And  such 
descriptions  may  be  given :  an  animal  is  an  organized 
body  having  sensation  and  volition ;  man  is  a  reasonable 
animal.  Whether  or  no  we  assent  to  the  exactness  of 
these  definitions,  we  allow  the  propriety  of  their  form. 
If  we  maintain  these  to  be  wrong,  we  must  believe  some 
others  to  be  right,  however  difficult  it  may  be  to  hit  upon 
them.  We  entertain  a  conviction  that  there  must  be, 
among  things  so  classed  and  named,  a  possibility  of  defin- 
ing each. 

Now  what  is  the  foundation  of  this  postulate  ?  What 
is  the  ground  of  this  assumption,  that  there  must  exist  a 
definition  which  we  have  never  seen,  and  which  perhaps 
no  one  has  seen  in  a  satisfactory  form  ?  The  knowledge 
of  this  definition  is  by  no  means  necessary  to  our  using 
the  word  with  propriety ;  for  any  one  can  make  true  asser- 
tions about  dogs,  but  who  can  define  a  dog  ?  And  yet  if 
the  definition  be  not  necessary  to  enable  us  to  use  the 
word,  why  is  it  necessary  at  all  ?  We  allow  that  we  pos- 
sess an  indestructible  conviction  that  there  must  be  such 
a  character  of  each  kind  as  will  supply  a  definition ;  but 
we  ask,  on  what  this  conviction  rests. 

I  reply,  that  our  persuasion  that  there  must  needs  be 
characteristic  marks  by  which  things  can  be  defined  in 


THE  IDEA  OF  LIKENESS.  459 

words,  is  founded  on  the  assumption  of  the  necessary  pos- 
sibility of  reasoning. 

The  reference  of  any  object  or  conception  to  its  class 
without  definition,  may  give  us  a  persuasion  that  it  shares 
the  properties  of  its  class,  but  does  not  enable  us  to  rea- 
son upon  those  properties.  When  we  consider  man  as 
an  animal,  we  ascribe  to  him  in  thought  the  appetites, 
desires,  affections,  which  we  habitually  include  in  our 
notion  of  animal :  but  except  we  have  expressed  these  in 
some  definition  or  acknowledged  description  of  the  term 
animal,  we  can  make  no  use  of  the  persuasion  in  ratioci- 
nation. But  if  we  have  described  animals  as  "beings 
impelled  to  action  by  appetites  and  passions,"  we  can  not 
only  think,  but  say,  "man  is  an  animal,  and  therefore  he 
is  impelled  to  act  by  appetites  and  passions."  And  if  we 
add  a  further  definition,  that  "  man  is  a  reasonable  ani- 
mal," and  if  it  appear  that  "reason  implies  conformity 
to  a  rule  of  action,"  we  can  then  further  infer  that  man's 
nature  is  to  conform  the  results  of  animal  appetite  and 
passion  to  a  rule  of  action. 

The  possibility  of  pursuing  any  such  Jtrain  of  reason- 
ing as  this,  depends  on  the  definitions,  of  animal  and  of 
man,  which  we  have  introduced ;  and  the  possibility  of 
reasoning  concerning  the  objects  around  us  being  inevit- 
ably assumed  by  us  from  the  constitution  of  our  nature, 
we  assume  consequently  the  possibility  of  such  definitions 
as  may  thus  form  part  of  our  deduction,  and  the  existence 
of  such  defining  characters. 

10.  Difficult!/  of  Definitions. — But  though  men  are,  on 
such  grounds,  led  to  make  constant  and  importunate 
demands  for  definitions  of  the  terms  which  they  employ 
in  their  speculations,  they  are,  in  fact,  far  from  being 
able  to  carry  into  complete  effect  the  postulate  on  which 
they  proceed,  that  they  must  be  able  to  find  definitions 
which  by  logical  consequence  shall  lead  to  the  truths 


460         PHILOSOPHY  OF  THE  CLASSIFICATORY  SCIENCES. 

they  seek.  The  postulate  overlooks  the  process  by  which 
our  classes  of  things  are  formed  and  our  names  applied. 
This  process  consisting,  as  we  have  already  said,  in 
observing  permanent  connexions  of  properties,  and  in 
fixing  them  by  the  attribution  of  names,  is  of  the  nature 
of  the  process  of  induction,  of  which  we  shall  afterwards 
have  to  speak.  And  the  postulate  is  so  far  true,  that 
this  process  of  induction  being  once  performed,  its  result 
may  usually  be  expressed  by  means  of  a  few  definitions, 
and  may  thus  lead  by  a  deduction  to  a  train  of  real  truths. 

But  in  the  subjects  where  we  principally  find  such  a 
subordination  of  classes  as  we  have  spoken  of,  this  pro- 
cess of  deduction  is  rarely  of  much  prominence :  for 
example,  in  the  branches  of  natural  history.  Yet  it  is 
in  these  subjects  that  the  existence  and  importance  of 
these  characteristic  marks,  which  we  have  spoken  of, 
principally  comes  into  view.  In  treating  of  these  marks, 
however,  we  enter  upon  methods  which  are  technical  and 
scientific,  not  popular  and  common.  And  before  we 
make  this  transition,  we  have  a  remark  to  make  on  the 
manner  in  which  writers,  without  reference  to  physics  or 
natural  history,  have  spoken  of  kinds,  their  subordination, 
and  their  marks. 

11.  "  The  Five  Words:'— These  things,— the  nature 
and  relations  of  classes, — were,  in  fact,  the  subjects  of 
minute  and  technical  treatment  by  the  logicians  of  the 
school  of  Aristotle.  Porphyry  wrote  an  Introduction  to 
the  Categories  of  that  philosoper,  which  is  entitled  On  the 
Five  Words.  The  "  Five  Words "  are  genus,  species, 
difference,  property,  accident.  Genus  and  species  are 
superior  and  inferior  classes,  and  are  stated*  to  be  capable 
of  repeated  subordination.  The  "most  general  genus" 
is  the  widest  class,  the  "  most  special  species "  the  nar- 
rowest. Between  these  are  intermediate  classes,  which 
*  PORPHYR.  Isagog.  c.  23. 


THE  IDEA  OF  LIKENESS.  461 

are  genera  with  regard  to  those  below,  and  species  with 
regard  to  those  above  them.  Thus  Being  is  the  most 
general  genus ;  under  this  is  Body  ;  under  Body  is  Living 
Body;  under  this  again  Animal ;  under  Animal  is  Rational 
Animal,  or  Man ;  under  Man  are  Socrates  and  Plato,  and 
other  individual  men. 

The  Difference  is  that  which  is  added  to  the  genus 
to  make  the  species ;  thus  Rational  is  the  Difference  by 
which  the  genus  Animal  is  made  the  species  Man ;  the 
Difference  in  this  Technical  sense  is  the  "  Specific,"  or 
species-making  Difference*.  It  forms  the  Definition  for 
the  purposes  of  logic,  and  corresponds  to  the  "  Character" 
(specific  or  generic)  of  the  Natural  Historians.  Indeed 
several  of  them,  as,  for  instance,  Linnaeus,  in  his  Philoso- 
plda  Botanica^  always  call  these  Characters  the  Difference, 
by  a  traditional  application  of  the  Peripatetic  terms  of  art. 

Of  the  other  two  words,  the  Property  is  that  which 
though  not  employed  in  defining  the  class,  belongs  to 
every  part  of  itf :  it  is,  "  What  happens  to  all  the  class, 
to  it  alone,  and  at  all  times  ;  as  to  be  capable  of  laughing 
is  a  property  of  a  man." 

The  Accident  is  that  which  may  be  present  and  absent 
without  the  destruction  of  the  subject,  as  to  sleep  is  an 
Accident  (a  thing  which  happens)  to  man. 

I  need  not  dwell  further  on  this  system  of  techni- 
calities. The  most  remarkable  points  in  it  are  those 
which  I  have  already  noticed ;  the  doctrine  of  the  succes- 
sive subordination  of  genera,  and  the  fixing  attention 
upon  the  specific  difference.  These  doctrines,  though 
invented  in  order  to  make  reasoning  more  systematic, 
and  at  a  period  anterior  to  the  existence  of  any  classifi- 
catory  science,  have,  by  a  curious  contrast  with  the  inten- 
tions of  their  founders,  been  of  scarcely  any  use  in  sciences 
of  reasoning,  but  have  been  amply  applied  and  developed 
*  etdoTrotoy.  f  Isagog.  c.  4. 


462        PHILOSOPHY  OP  THE  CLASSIFICATORY  SCIENCES 

in  the  Natural  History  which  arose  in  later  times.  We 
must  now  treat  of  the  principles  on  which  this  science 
proceeds,  and  explain  what  peculiar  arid  technical  pro- 
cesses it  employs  in  addition  to  those  of  common  thought 
and  common  language. 


CHAPTER  II. 

THE  METHODS  OF  NATURAL  HISTORY,  AS  REGU- 
LATED BY  THE  IDEA  OF  LIKENESS. 

1.  Idea  of  Likeness  in  Natural  History. — The  various 
branches  of  Natural  History,  in  so  far  as  they  are  classi- 
ficatory  sciences  merely,  and  do  not  depend  upon  physio- 
logical views,  rest  upon  the  same  Idea  of  Likeness  which 
is  the  ground  of  the  application  of  the  names,  more  or 
less  general,  of  common  language.  But  the  nature  of 
science  requires  that  for  her  purposes  this  idea  should  be 
applied  in  a  more  exact  and  rigorous  manner  than  in  its 
common  and  popular  employment ;  just  as  occurs  with 
regard  to  the  other  Ideas  on  which  science  is  founded ;— • 
for  instance,  as  the  idea  of  space  gives  rise,  in  popular  use, 
to  the  relations  implied  in  the  prepositions  and  adjectives 
which  refer  to  position  and  form,  and  in  its  scientific 
developement  gives  rise  to  the  more  precise  relations  of 
geometry. 

The  way  in  which  the  Idea  of  Likeness  has  been 
applied,  so  as  to  lead  to  the  construction  of  a  science,  is 
best  seen  in  Botany :  for,  in  the  Classification  of  Animals, 
we  are  inevitably  guided  by  a  consideration  of  the  function 
of  parts ;  that  is,  by  an  idea  of  purpose,  and  not  of  like- 
ness merely :  and  in  Mineralogy  the  attempts  at  classifi- 
cation on  the  principles  of  Natural  History  have  been 
hitherto  very  imperfectly  successful.  But  in  Botany  we 
have  an  example  of  a  branch  of  knowledge  in  which  sys- 


METHODS  OF  NATURAL  HISTORY.  463 

teiAatic  classification  has  been  effected  with  great  beauty 
and  advantage;  and  in  which  the  peculiarities  and  prin- 
ciples on  which  such  classification  must  depend  have  been 
carefully  studied.  Many  of  the  principal  botanists,  as 
Linnaeus,  Adanson,  Decandolle,  have  not  only  practically 
applied,  but  have  theoretically  enunciated,  what  they  held 
to  be  the  sound  maxims  of  classificatory  science:  and 
have  thus  enabled  us  to  place  before  the  reader  with  con-» 
fidence  the  philosophy  of  this  kind  of  science. 

2.  Condition  of  its  Use. — We  may  begin  by  remarking 
that  the  Idea  of  Likeness,  in  its  systematic  employment, 
is  governed  by  the  same  principle  which  we  have  already 
spoken  of   as  regulating  the  distribution  of  things  into 
kinds,   and  the  assignment   of  names   in   unsystematic 
thought  and  speech ;  namely,  the  condition  that  general 
propositions  shall  be  possible.     But  as  in  this  case  the  pro- 
positions are  tof  be  of  a  scientific  form  and  exactness,  the 
likeness  must  be  treated  with  a  corresponding  precision ; 
and  its  consequences  traced  by  steady  and  distinct  pro- 
cesses.    Naturalists  must,  for  their  purposes,  employ  the 
resemblances  of  objects  in  a  technical  manner.     This  tech- 
nical process  may  be  considered  as  consisting  of  three 
steps; — The  fixation  of  the  resemblances;  The  use  of 
them  in  making  a  classification ;  The  means  of  applying 
the  classification.     These  three  steps  may  be  spoken  of  as 
the  Terminology,  the  Plan  of  the  System,  and  the  Scheme 
of  the  Characters. 

3.  (I.)  Terminology*. — Terminology  signifies  the  col- 
lection of  terms,  or  technical  words,  which  belong  to  the 
science.     But  in   fixing  the  meaning  of  the  terms,  at 

*  Decandolle  and  others  use  the  term  Glossology  instead  of  Termi- 
nology, to  avoid  the  blemish  of  a  word  compounded  of  two  parts  taken 
from  different  languages.  The  convenience  of  treating  the  termina- 
tion ology  (and  a  few  other  parts  of  compounds)  as  not  restricted  to 
Greek  combinations,  is  so  great,  that  I  shall  venture,  in  these  cases,  to 
disregard  this  philological  scruple. 


464       PHILOSOPHY  OF  THE  CLASSIFICATORY  SCIENCES. 

least  of  the  descriptive  terms,  we  necessarily  fix,  at  the 
same  time,  the  perceptions  and  notions  which  the  terms 
are  to  convey ;  and  thus  the  terminology  of  a  classifica- 
tory  science  exhibits  the  elements  of  its  substance  as 
well  as  of  its  language.  A  large  but  indispensable  part 
of  the  study  of  botany  (and  of  mineralogy  and  zoology 
also,)  consists  in  the  acquisition  of  the  peculiar  voca- 
bulary of  the  science. 

The  meaning  of  technical  terms  can  be  fixed  in  the 
first  instance  only  by  convention,  and  can  be  made  intel- 
ligible only  by  presenting  to  the  senses  that  which  the 
terms  are  to  signify.  The  knowledge  of  a  colour  by  its 
name  can  only  be  taught  through  the  eye.  No  descrip- 
tion can  convey  to  a  hearer  what  we  mean  by  apple  green 
or  French  grey.  It  might,  perhaps,  be  supposed  that,  in 
the  first  example,  the  term  apple,  referring  to  so  familiar 
an  object,  sufficiently  suggests  the  colour  intended.  But 
it  may  easily  be  seen  that  this  is  not  true ;  for  apples  are 
of  many  different  hues  of  green,  and  it  is  only  by  a  con- 
ventional selection  that  we  can  appropriate  the  term  to 
one  special  shade.  When  this  appropriation  is  once  mad  e, 
the  term  refers  to  the  sensation,  and  not  to  the  parts  of 
the  term ;  for  these  enter  into  the  compound  merely  as 
a  help  to  the  memory,  whether  the  suggestion  be  a 
natural  connexion  as  in  "apple  green,"  or  a  casual  one  as  in 
"French  grey."  In  order  to  derive  due  advantage  from 
technical  terms  of  this  kind,  they  must  be  associated 
immediately  with  the  perception  to  which  they  belong ; 
and  not  connected  with  it  through  the  vague  usages  of 
common  language.  The  memory  must  retain  the  sensa- 
tion; and  the  technical  word  must  be  understood  as 
directly  as  the  most  familiar  word,  and  more  distinctly. 
When  we  find  such  terms  as  tin-white  or  pinchbeck- 
brown,  the  metallic  colour  so  denoted  ought  to  start  up 
in  our  memory  without  delay  or  search. 


METHODS  OF  NATURAL  HISTORY.  465 

This,  which  it  is  most  important  to  recollect  with 
respect  to  the  simpler  properties  of  bodies,  as  colour  and 
form,  is  no  less  true  with  respect  to  more  compound 
notions.  In  all  cases  the  term  is  fixed  to  a  peculiar 
meaning  by  convention ;  and  the  student,  in  order  to  use 
the  word,  must  be  completely  familiar  with  the  conven- 
tion, so  that  he  has  no  need  to  frame  conjectures  from 
the  word  itself.  Such  conjectures  would  always  be  inse- 
cure, and  often  erroneous.  Thus  the  term  papilionaceous 
applied  to  a  flower  is  employed  to  indicate,  not  only  a  re- 
semblance to  a  butterfly,  but  a  resemblance  arising  from 
five  petals  of  a  certain  peculiar  shape  and  arrangement ; 
and  even  if  the  resemblance  were  much  stronger  than  it 
is  in  such  cases,  yet  if  it  were  produced  in  a  different  way, 
as,  for  example,  by  one  petal,  or  two  only,  instead  of  a 
"  standard,"  two  "  wings,"  and  a  "  keel"  consisting  of  two 
parts  more  or  less  united  into  one,  we  should  no  longer 
be  justified  in  speaking  of  it  as  a  "  papilionaceous"  flower. 

The  formation  of  an  exact  and  extensive  descriptive 
language  for  botany  has  been  executed  with  a  degree  of 
skill  and  felicity,  which,  before  it  was  attained,  could 
hardly  have  been  dreamt  of  as  attainable.  Every  part  of 
a  plant  has  been  named ;  and  the  form  of  every  part,  even 
the  most  minute,  has  had  a  large  assemblage  of  descrip- 
tive terms  appropriated  to  it,  by  means  of  which  the 
botanist  can  convey  and  receive  knowledge  of  form  and 
structure,  as  exactly  as  if  each  minute  part  were  pre- 
sented to  him  vastly  magnified.  This  acquisition  w^as 
part  of  the  Linnaean  reform,  of  which  we  have  spoken  in 
the  History.  "  Tournefort,"  says  Decandolle*,  "  appears  to 
have  been  the  first  who  really  perceived  the  utility  of  fixing 
the  sense  of  terms  in  such  a  way  as  always  to  employ  the 
same  word  in  the  same  sense,  and  always  to  express  the 
same  idea  by  the  same  word ;  but  it  was  Linnaeus  who 

*  Theor.  Elem.,  p.  327. 
VOL.  I.  2  H 


466        PHILOSOPHY  OF  THE  CLASSIFICATORY  SCIENCES. 

really  created  and  fixed  this  botanical  language,  and 
this  is  his  fairest  claim  to  glory,  for  by  this  fixation  of 
language  he  has  shed  clearness  and  precision  over  all 
parts  of  the  science." 

It  is  not  necessary  here  to  give  any  detailed  account 
of  the  terms  of  botany.  The  fundamental  ones  have  been 
gradually  introduced,  as  the  parts  of  plants  were  more 
carefully  and  minutely  examined.  Thus  the  flower  was 
successively  distinguished  into  the  calyx,  the  corolla,  the 
stamens,  and  the  pistils :  the  sections  of  the  corolla  were 
termed  petals  by  Columna;  those  of  the  calyx  were 
called  sepals  by  Necker*.  Sometimes  terms  of  greater 
generality  were  devised ;  as  perianth  to  include  the  calyx 
and  corolla,  whether  one  or  both  of  these  were  present  f; 
pericarp  for  the  part  inclosing  the  grain,  of  whatever  kind 
it  be,  fruit,  nut,  pod,  &c.  And  it  may  easily  be  imagined 
that  descriptive  terms  may,  by  definition  and  combination, 
become  very  numerous  and  distinct.  Thus  leaves  may  be 
called  pinnatifid\,  pinnatipartite,  pinnatisect,  pinnatilobate, 
palmatifid,  palmatipartite,  &c.,  and  each  of  these  words 
designates  different  combinations  of  the  modes  and  extent 
of  the  divisions  of  the  leaf  with  the  divisions  of  its  outline. 
In  some  cases  arbitrary  numerical  relations  are  introduced 
into  the  definition :  thus  a  leaf  is  called  bilobatej  when  it 
is  divided  into  two  parts  by  a  notch ;  but  if  the  notch  go 
to  the  middle  of  its  length,  it  is  bifid ;  if  it  go  near  the 
base  of  the  leaf,  it  is  bipartite ;  if  to  the  base,  it  is  bisect. 
Thus,  too,  a  pod  of  a  cruciferous  plant  is  a  silica\\  if  it  be 
four  times  as  long  as  it  is  broad,  but  if  it  be  shorter  than 
this  it  is  a  silicula.  Such  terms  being  established,  the 
form  of  the  very  complex  leaf  or  frond  of  a  fern  is  exactly 
conveyed  by  the  following  phrase :  "  fronds  rigid  pinnate, 

*  DEC.  329. 

t  For  this  Erliart  and  Decandolle  use  Perigone. 

%  DEC.  318.  §  Ib.  493.  ||  Ib.  422. 


METHODS  OF  NATURAL  HISTORY.  467 

pinnae   recurved    subunilateral   pinnatifid,  the   segments 
linear  undivided  or  bifid  spinuloso-serrate*." 

Other  characters,  as  well  as  form,  are  conveyed  with 
the  like  precision :  Colour  by  means  of  a  classified  scale 
of  colours,  as  we  have  seen  in  speaking  of  the  measures 
of  secondary  qualities ;  to  which,  however,  we  must  add, 
that  the  naturalist  employs  arbitrary  names,  (such  as  we 
have  already  quoted,)  and  not  mere  numerical  exponents, 
to  indicate  a  certain  number  of  selected  colours.  This 
was  done  with  most  precision  by  Werner,  and  his  scale 
of  colours  is  still  the  most  usual  standard  of  naturalists. 
Werner  also  introduced  a  more  exact  terminology  with 
regard  to  other  characters  which  are  important  in  mine- 
ralogy, as  lustre,  hardness.  But  Mohs  improved  upon  this 
step  by  giving  a  numerical  scale  of  hardness,  in  which 
talc  is  1,  gypsum  2,  calc  spar  3,  and  so  on,  as  we  have 
already  explained  in  the  History  of  Mineralogy.  Some 
properties,  as  specific  gravity,  by  their  definition  give  at 
once  a  numerical  measure ;  and  others,  as  crystalline 
form,  require  a  very  considerable  array  of  mathematical 
calculation  and  reasoning,  to  'point  out  their  relations 
and  gradations.  In  all  cases  the  features  of  likeness  in 
the  objects  must  be  rightly  apprehended,  in  order  to  their 
being  expressed  by  a  distinct  terminology.  Thus  no 
terms  could  describe  crystals  for  any  purpose  of  natural 
history,  till  it  was  discovered  that  in  a  class  of  minerals 
the  proportion  of  the  faces  might  vary,  while  the  angle 
remained  the  same.  Nor  could  crystals  be  described  so 
as  to  distinguish  species,  till  it  was  found  that  the  de- 
rived and  primitive  forms  are  connected  by  very  simple 
relations  of  space  and  number.  The  discovery  of  the 
mode  in  which  characters  must  be  apprehended  so  that 
they  may  be  considered  w&  fixed  for  a  class,  is  an  important 

*  HOOKER,  Brit.  Flo.,  p.  450.  Hymenophyllum  Wilsoni,  Scot- 
tish filmy-fern,  abundant  in  the  Highlands  of  Scotland  and  about 
Killarney.  2  H  2 


468      PHILOSOPHY  OF  THE  CLASSIFICATORY  SCIENCES. 

step  in  the  progress  of  each  branch  of  Natural  History  ; 
and  hence  we  have  had,  in  the  History  of  Mineralogy 
and  Botany,  to  distinguish  as  important  and  eminent 
persons  those  who  made  such  discoveries,  Rome  de 
Lisle  and  Hauy,  Cesalpinus  and  Gesner. 

By  the  continued  progress  of  that  knowledge  of 
minerals,  plants,  and  other  natural  objects,  in  which  such 
persons  made  the  most  distinct  and  marked  steps,  but 
which  has  been  constantly  advancing  in  a  more  gradual 
and  imperceptible  manner,  the  most  important  and  essen- 
tial features  of  similarity  and  dissimilarity  in  such  objects 
have  been  selected,  arranged,  and  fitted  with  names ;  and 
we  have  thus  in  such  departments,  systems  of  terminology 
which  fix  our  attention  upon  the  resemblances  which  it 
is  proper  to  consider,  and  enable  us  to  convey  them  in 
words.  We  have  now  to  speak  of  the  mode  in  which 
such  resemblances  have  been  employed  in  the  construc- 
tion of  a  systematic  classification. 

4.  (II.)  The  Plan  of  the  System.— The  collection  of 
sound  views  and  maxims  by  which  the  resemblances  of 
natural  objects  are  applied  so  as  to  form  a  scientific  classi- 
fication, is  a  department  of  the  philosophy  of  natural  history 
which  has  been  termed  by  some  writers  (as  Decandolle,) 
Taxonomy,  as  containing  the  Laws  of  the  Taxis,  (arrange- 
ment). By  some  Germans  this  has  been  denominated 
Systematik ;  if  we  could  now  form  a  new  substantive  after 
the  analogy  of  the  words  Logic,  Rhetoric,  and  the  like, 
we  might  call  it  Systematic^.  But  though  our  English 
writers  commonly  use  the  expression  Systematical  Botany 
for  the  Botany  of  Classification,  they  appear  to  prefer 
the  term  Diatcuvis  for  the  method  of  constructing  the 
classification.  The  rules  of  such  a  branch  of  science  are 
curious  and  instructive. 

In  framing  a  classification  of  objects  we  must  attend 
to  their  resemblances  and  differences.  But  here  the 
question  occurs,  to  ivhat  resemblances  and  differences?  for 


METHODS  OF  NATURAL  HISTORY.  469 

a  different  selection  of  the  points  of  resemblance  would 
give  different  results  :  a  plant  frequently  agrees  in  leaves 
with  one  group  of  plants,  in  flowers  with  another.  Which 
set  of  characters  are  we  to  take  as  our  guide  ? 

The  view  already  given  of  the  regulative  principle  of 
all  classification,  namely,  that  it  must  enable  us  to  assert 
true  and  general  propositions,  will  obviously  occur  as 
applicable  here.  The  object  of  a  scientific  classification 
is  to  enable  us  to  enunciate  scientific  truths :  we  must 
therefore  classify  according  to  those  resemblances  of 
objects  (plants  or  any  others,)  which  bring  to  light  such 
truths. 

But  this  reply  to  the  inquiry,  On  what  characters  of 
resemblance  we  are  to  found  our  system,  is  still  too  gene- 
ral and  vague  to  be  satisfactory.  It  carries  us,  however,  as 
far  as  this ;  that  since  the  truths  we  are  to  attend  to  are 
scientific  truths,  governed  by  precise  and  homogeneous 
relations,  we  must  not  found  our  scientific  classification  on 
casual,  indefinite,  and  unconnected  considerations.  We 
must  not,  for  instance,  be  satisfied  with  dividing  plants, 
as  Dioscorides  does,  into  aromatic,  esculent,  medicinal, 
and  vinous ;  or  even  with  the  long  prevalent  distribution 
into  trees,  shrubs,  and  herbs ;  since  in  these  subdivisions 
there  is  no  consistent  principle. 

5.  Latent  Reference  to  Natural  Affinity. — But  there 
may  be  several  kinds  of  truths,  all  exact  and  coherent, 
which  may  be  discovered  concerning  plants  or  any  other 
natural  objects  ;  and  if  this  should  be  the  case,  our  rule 
leaves  us  still  at  a  loss  in  what  manner  our  classification 
is  to  be  constructed.  And,  historically  speaking,  a  much 
more  serious  inconvenience  has  been  this ; — that  the  task 
of  classification  of  plants  was  necessarily  performed  when 
the  general  laws  of  their  form  and  nature  were  very  little 
known  ;  or  rather,  when  the  existence  of  such  laws  was 
only  just  beginning  to  be  discerned.  Even  up  to  the 
present  day,  the  general  propositions  which  botanists  are 


470       PHILOSOPHY  OF  THE  CLASSIFICATORY  SCIENCES. 

able  to  assert  concerning  the  structure  and  properties  of 
plants,  are  extremely  imperfect  and  obscure. 

We  are  thus  led  to  this  conclusion : — that  the  idea  of 
likeness  could  not  be  applied  so  as  to  give  rise  to  a  scien- 
tific classification  of  plants,  till  considerable  progress  was 
made  in  studying  the  general  relations  of  vegetable  form 
and  life ;  and  that  the  selection  of  the  resemblances  which 
should  be  taken  into  account,  must  depend  upon  the 
nature  of  the  relations  which  were  then  brought  into  view. 

But  this  amounts  to  saying  that,  in  the  consideration  of 
the  classification  of  vegetables,  other  Ideas  must  be  called 
into  action  as  well  as  the  Idea  of  Likeness.  The  new 
general  views  to  which  the  more  intimate  study  of  plants 
leads,  must  depend,  like  all  general  truths,  upon  some 
regulating  Idea  which  gives  unity  to  scattered  facts :  no 
progress  could  be  made  in  botanical  knowledge  without 
the  operation  of  such  principles :  and  such  additional 
Ideas  must  be  employed,  besides  those  of  mere  likeness 
and  unlikeness,  in  order  to  point  out  that  classification 
which  has  a  real  scientific  value. 

Accordingly  in  the  classificatory  sciences  Ideas  other 
than  Likeness  do  make  their  appearance.  Such  Ideas 
in  botany  have  influenced  the  progress  of  the  science, 
even  before  they  have  been  clearly  brought  into  view. 
We  have  especially  the  Idea  of  Affinity,  which  is  the 
basis  of  all  Natural  Systems  of  Classification,  and 'which 
we  shall  consider  in  a  succeeding  chapter.  The  assump- 
tion that  there  is  a  Natural  System,  an  assumption  made 
by  all  philosophical  botanists,  implies  a  belief  in  the 
existence  of  Natural  Affinity,  and  is  carried  into  effect  by 
means  of  principles  which  are  involved  in  that  Idea. 
But  as  the  formation  of  all  systems  of  classification  must 
involve,  in  a  great  degree,  the  Idea  of  Resemblance  and 
Difference,  I  shall  first  consider  the  effect  of  that  Idea, 
before  I  treat  specially  of  Natural  Affinity. 

6.  Natural  Classes. — Many  attempts  were   made  to 


METHODS  OF   NATURAL  HISTORY.  471 

classify  vegetables  before  the  rules  which  govern  a  natural 
system,  were  clearly  apprehended.  Botanists  agreed  in 
esteeming  some  characters  as  of  more  value  than  others, 
before  they  had  agreed  upon  any  general  rules  or  prin- 
ciples for  estimating  the  relative  importance  of  the  cha- 
racters. They  were  convinced  of  the  necessity  of  adding 
other  considerations  to  that  of  resemblance,  without  see- 
ing clearly  what  these  ought  to  be.  They  aimed  at  a 
Natural  Classification,  without  knowing  distinctly  in  what 
manner  it  was  to  be  Natural. 

The  attempts  to  form  Natural  Classes,  therefore,  in  the 
first  part  of  their  history,  belong  to  the  Idea  of  Likeness, 
though  obscurely  modified,  even  from  an  earty  period,  by 
the  Ideas  of  Affinity,  and  even  of  Function  and  of  Deve- 
lopement.  Hence  Natural  Classes  may,  to  a  certain 
extent  be  treated  of  in  this  place. 

Natural  Classes  are  opposed  to  Artificial  Classes,  which 
are  understood  to  be  regulated  by  an  assumed  character. 
Yet  no  classes  can  be  so  absolutely  Artificial  in  this 
sense,  as  to  be  framed  upon  characters  arbitrarily  as- 
sumed ;  for  instance,  no  one  would  speak  of  a  class  of 
shrubs  defined  by  the  circumstance  of  each  having  a 
hundred  leaves :  for  of  such  a  class  no  assertion  could  be 
made,  and  therefore  the  class  could  never  come  under  our 
notice.  In  what  sense  then  are  Artificial  Classes  to  be 
understood,  as  opposed  to  Natural  ? 

7.  Artificial  Classes. — To  this  question  the  following 
is  the  answer.  When  Natural  Classes  of  a  certain  small 
extent  have  been  formed,  a  system  may  be  devised  which 
shall  be  regulated  by  a  few  selected  characters,  and  which 
shall  not  dissever  these  small  Natural  Classes,  but  con- 
form to  them  as  far  as  they  go.  If  these  selected 
characters  be  made  absolute  and  imperative,  and  if  we 
abandon  all  attempt  to  obtain  Natural  Classes  of  any 
higher  order  and  wider  extent,  we  form  an  Artificial 
System. 


472       PHILOSOPHY  OF  THE  CLASSIFICATORY  SCIENCES. 

Thus  in  the  Linneean  System  of  Botanical  Classifica- 
tion, it  is  assumed  that  certain  natural  groups,  namely, 
species  and  genera,  are  established  ;  it  is  conceived,  more- 
over, that  the  division  of  classes  according  to  the  number 
of  stamens  and  of  pistils  does  not  violate  the  natural 
connexions  of  species  and  genera.  This  arrangement, 
according  to  the  number  of  stamens  and  pistils,  (further 
modified  in  certain  cases  by  other  considerations,)  is  then 
made  the  ground  of  all  the  higher  divisions  of  plants,  and 
thus  we  have  an  Artificial  System. 

It  has  been  objected  to  this  view,  that  the  Linnsean 
Artificial  System  does  not  in  all  cases  respect  the  boun- 
daries of  genera,  but  would,  if  rigorously  applied,  distribute 
the  species  of  the  same  genus  into  different  artificial 
classes ;  it  would  divide,  for  instance,  the  genera  Vale- 
riana,  Geranium*,  &c.  To  this  we  must  reply,  that  so 
far  as  the  Linnsean  System  does  this,  it  is  an  imperfect 
Artificial  System.  Its  great  merit  is  in  its  making  such  a 
disjunction  in  comparatively  so  few  cases;  and  in  the  ar- 
tificial characters  being,  for  the  most  part,  obvious  and 
easily  applied. 

8.  Are  Genera  Natural  f — It  has  been  objected  also 
that  Genera  are  not  Natural  groups.  Linnaeus  asserts  in 
the  most  positive  manner  that  they  aref.  On  which 
Adanson  observes!,  "I  know  not  how  any  Botanist  can 
maintain  such  a  thesis :  that  which  is  certain  is,  that  up 
to  the  present  time  no  one  has  been  able  to  prove  it,  nor 
to  give  an  exact  definition  of  a  natural  genus,  but  only  of 
an  artificial."  He  then  brings  several  arguments  to  con- 
firm this  view. 

But  we  are  to  observe,  in  answer  to  this,  that  Adan- 
son improperly  confounds  the  recognition  of  the  existence 
of  a  natural  group  with  the  invention  of  a  technical 
mark  or  definition  of  it.  Genera  are  groups  of  species 

*  DECAND.  Th.  EL,  p.  45. 
t  P/iil.  J3ot.    Art.  165.  $  Famille  de  Ph.,  Pref.  cv. 


METHODS  OF  NATURAL  HISTORY.  473 

associated  in  virtue  of  natural  affinity,  of  general  resem- 
blance, of  real  propinquity:  of  such  groups,  certain 
selected  characters,  one  or  few,  may  usually  be  discovered, 
by  which  the  species  may  be  referred  to  their  groups. 
These  Artificial  characters  do  not  constitute,  but  indicate 
the  genus :  they  are  the  Diagnosis,  not  the  basis  of  the 
Diataxis:  and  they  are  always  subject  to  be  rejected,  and 
to  have  others  substituted  for  them,  when  they  violate 
the  natural  connexion  of  species  which  a  minute  and 
enlarged  study  discovers.  * 

It  is,  therefore,  no  proof  that  Genera  are  not  Natural, 
to  say  that  their  artificial  characters  are  different  in  dif- 
ferent systems.     Such  characters  are  only  different  at- 
tempts to  confine  the  variety  of  nature  within  the  limits 
of  definition.     Nor  is  it  sufficient  to  say  that  these  groups 
themselves  are  different  in  different  writers ;  that  some 
botanists  make  genera  what  others  make  only  species ;  as 
Pedicularis,  Rhinanthus,  Euphrasies  Antirrhinmi*.     This 
discrepancy  shows  only  that  the  natural  arrangement  is 
not  yet  completely  known,  even  in  the  smaller  groups ; 
a  conclusion  to  which  we  need  not  refuse  our  assent. 
But  in  opposition  to  these  negatives,  the  manner  in  which 
Genera  have  been  established  proves  that  they  are  regu- 
lated by  the  principle  of  being  natural  and  that  alone. 
For  they  are  not  formed  according  to  any  a  priori  rule. 
The  Botanist  does  not  take  any  selected  or  arbitrary  part 
or  parts  of  the  plants,  and  marshal  his  genera  according 
to   the   differences  of  this  part.     On  the  contrary,  the 
divisions  of  genera  are  sometimes  made  by  means  of  the 
flower ;    sometimes  by  means  of  the  fruit ;    the  anthers, 
the  stamens,  the  seeds,  the  pericarp,  and  the  most  varied 
features  of  these  parts,  are  used  in  the  most  miscellaneous 
and  unsystematic   manner.       Linnaeus   has  indeed   laid 
down   a   maxim    that   the   characteristic    differences   of 

*  ADANSON,  p.  cvi. 


474        PHILOSOPHY  OF  THE  CLASSIFICATORY  SCIENCES. 

genera  must  reside  in  the  fructification5*:  but  Adanson 
has  justly  remarked  f,  that  an  arbitrary  restriction  like 
this  makes  the  groups  artificial :  and  that  in  some  families 
other  characters  are  more  essential  than  those  of  the 
fructification ;  as  the  leaves  in  the  families  of  Aparinea 
and  LeguminoscB,  and  the  disposition  of  the  flowers  in 
Labiatce.  And  Naturalists  are  so  far  from  thinking  it 
sufficient  to  distribute  species  into  genera  by  arbitrary 
marks,  that  we  find  them  in  many  cases  lamenting  the 
absence  of  good  natural  marks:  as  in  the  families  of 
Umbelliferee,  where  Linnaeus  declared  that  any  one  who 
could  find  good  characters  of  genera  would  deserve  great 
admiration,  and  where  it  is  only  of  late  that  good 
characters  have  been  discovered  and  the  arrangement 
settled  £  by  means  principally  of  the  ribs  of  the  fruit  J. 

It  is  thus  clear  that  genera  are  not  established  on  any 
assumed  or  preconceived  basis.  What,  then,  is  the  prin- 
ciple which  regulates  botanists  when  they  try  to  fix 
genera  ?  What  is  the  arrangement  which  they  thus  wish 
for,  without  being  able  to  hit  upon  it?  What  is  the 
tendency  which  thus  drives  them  from  the  corolla  to  the 
anthers,  from  the  flower  to  the  fruit,  from  the  fructifica- 
tion to  the  leaves  ?  It  is  plain  that  they  seek  something, 
not  of  their  own  devising  and  creating ; — not  anything 
merely  conventional  and  systematic;  but  something  which 
they  conceive  to  exist  in  the  relations  of  the  plants 
themselves ; — something  which  is  without  the  mind,  not 
within ; — in  nature,  not  in  art ; — in  short,  a  natural  order. 

Thus  the  regulative  principle  of  a  genus,  or  of  any 
other  natural  group  is,  that  it  is,  or  is  supposed  to  be, 
natural.  And  by  reference  to  this  principle  as  our  guide, 

*  Phil.  Bot.     Art.  162.  t  ADANSON,  Pref.,  p.  cxx. 

J  LINDLEY,  Nat.  Syst.y  p.  5. 

§  In  like  manner  we  find  Cuvier  saying  of  Rondelet  that  he  has 
"  un  sentiment  tres  vrai  des  genres."     Hist.  Ichth.,  p.  39. 


METHODS  OF  NATURAL  HISTORY.  475 

we  shall  be  able  to  understand  the  meaning  of  that  inde- 
finiteness  and  indecision  which  we  frequently  find  in  the 
descriptions  of  such  groups,  and  which  must  appear  so 
strange  and  inconsistent  to  any  one  who  does  not  suppose 
these  descriptions  to  assume  any  deeper  ground  of  con- 
nexion than  an  arbitrary  choice  of  the  botanist.  Thus 
in  the  family  of  the  Rose-tree,  we  are  told  that  the 
ovules  are  very  rarely  erect*,  the  stigmata  usually  simple. 
Of  what  use,  it  might  be  asked,  can  such  loose  accounts 
be?  To  which  the  answer  is,  that  they  are  not  inserted 
in  order  to  distinguish  the  species,  but  in  order  to 
describe  the  family,  and  the  total  relations  of  the  ovules 
and  of  the  stigmata  of  the  family  are  better  known  by 
this  general  statement.  A  similar  observation  may  be 
made  with  regard  to  the  Anomalies  of  each  group,  which 
occur  so  commonly,  that  Mr.  Lindley,  in  his  Introduction 
to  the  Natural  System  of  Botany,  makes  the  "Anomalies" 
an  article  in  each  family.  Thus,  part  of  the  character  of 
the  Rosaceae  is  that  they  have  alternate  stipulate  leaves, 
and  that  the  albumen  is  obliterated :  but  yet  in  Lowea,  one 
of  the  genera  of  this  family,  the  stipulae  are  absent ;  and 
the  albumen  is  present  in  another,  Neillia.  This  implies, 
as  we  have  already  seen,  that  the  artificial  character  (or 
diagnosis  as  Mr.  Lindley  calls  it)  is  imperfect.  It  is, 
though  very  nearly,  yet  not  exactly,  commensurate  with 
the  natural  group  :  and  hence  in  certain  cases  this  cha- 
racter is  made  to  yield  to  the  general  weight  of  natural 
affinities. 

9.  Difference  of  Natural  History  and  Mathematics. — 
These  views, — of  classes  determined  by  characters  which 
cannot  be  expressed  in  words, — of  propositions  which 
state,  not  what  happens  in  all  cases,  but  only  usually, — 
of  particulars  which  are  included  in  a  class  though  they 
transgress  the  definition  of  it,  may  very  probably  surprise 

•*  LINDLEY,  Nat.  Syst.,  p.  81. 


470        PHILOSOPHY  OF  THE  CLASSIFICATORY  SCIENCES. 

the  reader.     They  are  so  contrary  to  many  of  the  received 
opinions  respecting  the  use  of  definitions  and  the  nature 
of  scientific  propositions,  that  they  will  probably  appear 
to   many  persons    highly  illogical   and   unphilosophical. 
But  a  disposition  to  such  a  judgment  arises  in  a  great 
measure  from  this  ; — that  the  mathematical  and  mathe- 
matico-physical  sciences  have,  in  a  great  degree,  deter- 
mined men's  views  of  the  general  nature  and  form  of 
scientific  truth  ;  while  Natural  History  has  not  yet  had 
time  or  opportunity  to  exert  its  due  influence  upon  the 
current  habits  of  philosophizing.     The  apparent  indefi- 
niteness    and    inconsistency   of    the   classifications   and 
definitions  of  Natural   History  belongs,  in  a  far  higher 
degree,  to  all  other  except  mathematical  speculations: 
and  the  modes  in  which  approximations  to  exact  distinc- 
tions and  general  truths  have  been  made  in  Natural  His- 
tory, may  be  worthy  our  attention,  even  for  the  light  they 
throw  upon  the  best  modes  of  pursuing  truth  of  all  kinds. 
10.  Natural  Groups  given  by  Type  not  by  Definition. — 
The  further  developement  of  this  suggestion   must  be 
considered   hereafter.     But   we  may  here   observe,  that 
though  in  a  Natural  group  of  objects  a  definition  can  no 
longer  be  of  any  use  as  a  regulative  principle,  classes  are 
not,  therefore,  left  quite  loose,  without  any  certain  stand- 
ard or  guide.     The  class   is   steadily  fixed,  though   not 
precisely  limited;    it  is  given,  though  not  circumscribed ; 
it  is  determined,  not  by  a  boundary  line  without,  but  by  a 
central  point  within ;    not  by  what  it  strictly  excludes, 
but  by  what  it  eminently  includes;    by  an  example,  not 
by  a  precept ;    in  short,  instead  of  Definition  we  have  a 
Type  for  our  director. 

A  Type  is  an  example  of  any  class,  for  instance,  a 
species  of  a  genus,  which  is  considered  as  eminently  pos- 
sessing the  characters  of  the  class.  All  the  species 
which  have  a  greater  affinity  with  this  type-species  than 


METHODS  OF  NATURAL  HISTORY.  477 

with  any  others,  form  the  genus,  and  are  ranged  about 
it,  deviating  from  it  in  various  directions  and  different 
degrees.  Thus  a  genus  may  consist  of  several  species 
which  approach  very  near  the  type,  and  of  which  the 
claim  to  a  place  with  it  is  obvious ;  while  there  may  be 
other  species  which  straggle  further  from  this  central 
knot,  and  which  yet  are  clearly  more  connected  with  it 
than  with  any  other.  And  even  if  there  should  be  some 
species  of  which  the  place  is  dubious,  and  which  appear 
to  be  equally  bound  to  two  generic  types,  it  is  easily  seen 
that  this  would  not  destroy  the  reality  of  the  generic 
groups,  any  more  than  the  scattered  trees  of  the  inter- 
vening plain  prevent  our  speaking  intelligibly  of  the  dis- 
tinct forests  of  two  separate  hills. 

The  type-species  of  every  genus,  the  type-genus  of 
every  family,  is,  then,  one  which  possesses  all  the  cha- 
racters and  properties  of  the  genus  in  a  marked  and  pro- 
minent manner.  The  type  of  the  Rose  family  has  alter- 
nate stipulate  leaves,  wants  the  albumen,  has  the  ovules 
not  erect,  has  the  stigmata  simple,  and  besides  these 
features,  which  distinguish  it  from  the  exceptions  or 
varieties  of  its  class,  it  has  the  features  which  make  it 
prominent  in  its  class.  It  is  one  of  those  which  possess 
clearly  several  leading  attributes ;  and  thus,  though  we 
cannot  say  of  any  one  genus  that  it  must  be  the  type  of 
the  family,  or  of  any  one  species  that  it  must  be  the  type 
of  the  genus,  we  are  still  not  wholly  to  seek :  the  type 
must  be  connected  by  many  affinities  with  most  of  the 
others  of  its  group ;  it  must  be  near  the  centre  of  the 
crowd,  and  not  one  of  the  stragglers. 

11.  It  has  already  been  repeatedly  stated,  as  the 
great  rule  of  all  classification,  that  the  classification  must 
serve  to  assert  general  pi'opositions.  It  may  be  asked 
what  propositions  we  are  able  to  enunciate  by  means  of 
such  classifications  as  we  are  now  treating  of.  And  the 


478        PHILOSOPHY  OF  THE  CLASSIFICATORY  SCIENCES. 

answer  is,  that  the  collected  knowledge  of  the  characters, 
habits,  properties,  organization,  and  functions  of  these 
groups  and  families,  as  it  is  found  in  the  best  botanical 
works,  and  as  it  exists  in  the  minds  of  the  best  botanists, 
exhibits  to  us  the  propositions  which  constitute  the 
science,  and  to  the  expression  of  which  the  classification 
is  to  serve.  All  that  is  not  strictly  definition,  that  is,  all 
that  is  not  artificial  character,  in  the  descriptions  of  such 
classes,  is  a  statement  of  truths,  more  or  less  general, 
more  or  less  precise,  but  making  up,  together,  the  posi- 
tive knowledge  which  constitutes  the  science.  As  we 
have  said,  the  consideration  of  the  properties  of  plants  in 
order  to  form  a  system  of  classification,  has  been  termed 
Taxonomy,  or  the  Systematick  of  Botany ;  all  the  parts 
of  the  descriptions,  which,  taking  the  system  for  granted, 
convey  additional  information,  are  termed  the  Physio- 
graphy of  the  science;  and  the  same  terms  may  be 
applied  in  the  other  branches  of  Natural  History. 

12.  Artificial  and  Natural  Systems. — If  I  have  suc- 
ceeded in  making  it  apparent  that  an  artificial  system  of 
characters  necessarily  implies  natural  classes  which  are 
not  severed  by  the  artificial  marks,  we  shall  now  be 
able  to  compare  the  nature  and  objects  of  the  Artificial 
and  Natural  Systems ;  points  on  which  much  has  been 
written  in  recent  times. 

The  Artificial  System  is  one  which  is,  or  professes  to 
be,  entirely  founded  upon  marks  selected  according  to  the 
condition  which  has  been  stated,  of  not  violating  certain 
narrow  natural  groups ;  namely,  in  the  Linnsean  system, 
the  natural  genera  of  plants.  The  marks  which  form  the 
basis  of  the  system  are  applied  rigorously  and  universally 
without  any  further  regard  to  any  other  characters  or  in- 
dications of  affinity.  Thus  in  the  Linnsean  system,  which 
depends  mainly  on  the  number  of  male  organs  or  stamens, 
and  on  the  number  of  female  organs  or  styles,  the  largest 


METHODS  OF  NATURAL  HISTORY.  479 

divisions,  or  the  Classes,  are  arranged  according  to  the 
number  of  the  stamens,  and  are  monandria,  diandria,  tri- 
andria,  tetrandria,  pentandria,  hexandria,  and  so  on :  the 
names  being  formed  of  the  Greek  numerical  words,  and 
of  the  word  which  implies  male.  And  the  Orders  of  each 
of  these  Classes  are  distinguished  by  the  number  of  styles, 
and  are  called  m&tpgyma,  digynia^  trigynia>  and  so  on, 
the  termination  of  these  words  meaning  female.  And  so 
far  as  this  numerical  division  and  subdivision  go  on,  the 
system  is  a  rigorous  system,  and  strictly  artificial. 

But  the  condition  that  the  artificial  system  shall  leave 
certain  natural  affinities  untouched,  makes  it  impossible 
to  go  through  the  vegetable  kingdom  by  a  method  of 
mere  numeration  of  stamens  and  styles.  The  distinction 
of  flowers  with  twenty  and  with  thirty  stamens  is  not  a 
fixed  distinction:  flowers  of  one  and  the  same  kind, as  roses, 
have,  some  fewer  than  the  former,  some  more  than  the 
latter  number.  The  Artificial  System,  therefore,  must  be 
modified.  And  there  are  various  relations  of  connexion 
and  proportion  among  the  stamina  which  are  more  per- 
manent and  important  than  their  mere  number.  Thus 
flowers  with  two  longer  and  two  shorter  stamens  are  not 
placed  in  the  class  tetrandria,  but  are  made  a  separate 
class  iidynamia ;  those  with  four  longer  and  two  shorter 
are  in  like  manner  tetradynamia,  not  hexandria ;  those  in 
which  the  filaments  are  bound  into  two  bundles  are  dia- 
delphia.  All  these  and  other  classes  are  deviations  from 
the  plan  of  the  earlier  classes,  and  are  so  far  defects  of 
the  artificial  system ;  but  they  are  requisite  in  order  that 
it  may  leave  a  basis  of  natural  groups,  without  which  it 
would  not  be  a  system  of  vegetables.  And  as  the  divi- 
sion is  still  founded  on  some  properties  of  the  stamens, 
it  combines  not  ill  with  that  part  of  the  system  which 
depends  on  the  number.  The  classes  framed  in  virtue  of 
these  various  considerations  make  up  an  artificial  system 
which  is  tolerably  coherent. 


480        PHILOSOPHY  OF  THE  CLASSIFICATORY  SCIENCES. 

But  since  the  Artificial  System  thus  regards  natural 
groups,  in  what  does  it  differ  from  a  Natural  System  ? 
It  differs  in  this : — That  though  it  allows  certain  subor- 
dinate natural  groups,  it  merely  allows  these,  and  does 
not  endeavour  to  ascend  to  any  wider  natural  groups. 
It  takes  all  the  higher  divisions  of  its  scheme  from  its 
artificial  characters,  its  stamens  and  pistils,  without  look- 
ing to  any  natural  affinities.  It  accepts  natural  genera, 
but  it  does  not  seek  natural  families,  or  orders,  or  classes. 
It  assumes  natural  groups,  but  does  not  investigate  any ; 
it  forms  wider  and  higher  groups,  but  professes  to  frame 
them  arbitrarily. 

But  then,  on  the  other  hand,  the  question  occurs, 
this  being  the  case,  what  can  be  the  use  of  the  Artificial 
System?  If  its  characters,  in  the  higher  stages  of  clas- 
sification, be  arbitrary,  how  can  it  lead  us  to  the  natural 
relations  of  plants  ?  And  the  answer  is,  that  it  does  so 
in  virtue  of  the  original  condition,  that  there  shall  be 
certain  natural  relations  which  the  artificial  system  shall 
not  transgress ;  and  that  its  use  arises  from  the  facility 
with  which  we  can  follow  the  artificial  arrangement  as 
far  as  it  goes.  We  can  count  the  stamens  and  pistils, 
and  thus  we  know  the  Class  and  Order  of  our  plant ;  and 
we  have  then  to  discover  its  Genus  and  Species  by  means 
less  symmetrical  but  more  natural.  The  Artificial  Sys- 
tem, though  arbitrary  in  a  certain  degree,  brings  us  to  a 
Class  in  which  the  whole  of  each  genus  is  contained,  and 
there  we  can  find  the  proper  Genus  by  a  suitable  method 
of  seeking.  No  Artificial  System  can  conduct  us  into 
the  extreme  of  detail,  but  it  can  place  us  in  a  situation 
where  the  detail  is  within  our  reach.  We  cannot  find 
the  house  of  a  foreign  friend  by  its  latitude  and  longi- 
tude ;  but  we  may  be  enabled,  by  a  knowledge  of  the 
latitude  and  longitude,  to  find  the  city  in  which  he 
dwells,  or  at  least  the  island ;  and  we  then  can  reach  his 


• 

METHODS  OF  NATURAL  HISTORY.  481 

abode  by  following  the  road  or  exploring  the  locality. 
The  Artificial  System  is  such  a  method  of  travelling  by 
latitude  and  longitude  ;  the  Natural  System  is  that  which 
is  guided  by  a  knowledge  of  the  country. 

The  Natural  System,  then,  is  that  which  endeavours 
to  arrange  by  the  natural  affinities  of  objects  ;  and  more 
especially,  which  attempts  to  ascend  from  the  lower 
natural  groups  to  the  higher ;  as  for  example  from  genera 
to  natural  families,  orders,  and  classes.  But  as  we  have 
already  hinted,  these  expressions  of  natural  affinities, 
natural  groups,  and  the  like,  when  considered  in  refer- 
ence to  the  idea  of  resemblance  alone,  without  studying 
analogy  or  function,  are  very  vague  and  obscure.  We 
must  notice  some  of  the  attempts  which  were  made 
under  the  operation  of  this  imperfect  view  of  the  subject. 

13.  Modes  of  framing  Natural  Systems. — Decan- 
dolle*  distinguishes  the  attempts  at  Natural  Classifica- 
tions into  three  sorts  :  those  of  blind  trial,  (tatonnement,) 
those  of  general  comparison,  and  those  of  subordination  of 
characters.  The  two  former  do  not  depend  distinctly 
upon  any  principle,  except  resemblance ;  the  third  refers 
us  to  other  views,  and  must  be  considered  in  a  future 
chapter. 

Method  of  Blind  Trial. — The  notion  of  the  existence 
of  natural  classes  dependent  on  the  general  resemblance 
of  plants, — of  an  affinity  showing  itself  in  different  parts 
and  various  ways,- — though  necessarily  somewhat  vague 
and  obscure,  was  acted  upon  at  an  early  period,  as  we 
have  seen  in  the  formation  of  genera;  and  was  enunciated 
in  general  terms  soon  after.  Thus  Magnoliusf  says  that 
he  discerns  in  plants  an  affinity,  by  means  of  which  they 
may  be  arranged  in  families.  "  Yet  it  is  impossible  to 

*  Th.  EL,  art.  41. 

t  DEC.  Th.  EL,  art.  42.     PETRI  MAGNOLI,  Prodromus  Hist.  Gen. 
Plant.,  1189. 

VOL.  I.  21 


482       PHILOSOPHY  OF  THE  CLASSIFICATORY  SCIENCES. 

obtain  from  the  fructification  alone  the  Characters  of  these 
families ;  and  I  have  therefore  chosen  those  parts  of 
plants  in  which  the  principal  characteristic  marks  are 
found,  as  the  root,  the  stem,  the  flower,  the  seed.  In 
some  plants  there  is  even  a  certain  resemblance;  an 
affinity  which  does  not  consist  in  the  parts  considered 
separately,  but  in  their  totality ;  an  affinity  which  may  be 
felt  but  not  expressed ;  as  we  see  in  the  families  of  agri- 
monies and  cinquefoils,  which  every  botanist  will  judge 
to  be  related,  though  they  differ  by  their  roots,  their 
leaves,  their  flowers,  and  their  seeds." 

This  obscure  feeling  of  a  resemblance  on  the  whole, 
an  affinity  of  an  indefinite  kind,  appears  fifty  years  later 
in  Linnseus's  attempts.  "  In  the  Natural  Classification," 
he  says*,  "  no  a  priori  rule  can  be  admitted,  no  part  of 
the  fructification  can  be  taken  exclusively  into  considera- 
tion ;  but  only  the  simple  symmetry  of  all  its  parts." 
Hence  though  he  proposed  natural  families,  and  even 
stated  the  formation  of  such  families  to  be  the  first  and 
last  object  of  all  methods,  he  never  gave  the  characters 
of  those  groups,  or  connected  them  by  any  method.  He 
even  declared  it  to  be  impossible  to  lay  down  such  a 
system  of  characters.  This  persuasion  was  the  result  of 
his  having  refused  to  admit  into  his  mind  any  idea  more 
profound  than  that  notion  of  resemblance  of  which  he 
had  made  so  much  and  such  successful  use ;  he  would  not 
attempt  to  unravel  the  ideas  of  symmetry  and  of  function 
on  which  the  clear  establishment  of  natural  relations 
must  depend.  He  even  despised  the  study  of  the  inner 
organization  of  plants  ;  and  reckoned  f  the  Anatomici,  who 
studied  the  anatomy  and  physiology  of  plants  and  the 
laws  of  vegetation,  among  the  Botanophili,  the  mere 
amateurs  of  his  science. 

The  same  notion  of  general  resemblance  and  affinity, 

*  DEC.,  Th.  EL,  art.  42.  t  Phil.  Sot.,  s.  44. 


METHODS  OF  NATURAL  HISTORY.  483 

accompanied  with  the  same  vagueness,  is  to  be  found  in 
the  writer  who  least  participated  in  the  general  admiration 
of  Linnaeus,  Buffon.     Though  it  was  in  a  great  measure 
his  love  of  higher  views  which  made  him  dislike  what 
he  considered  the  pedantry   of  the  Swedish   school,  he 
does  not  seem  to  have  obtained  a  clearer  sight  of  the 
principle  of  the  natural  method   than  his  rival,  except 
that  he  did  not  restrict  his  Characters  to  the  fructification. 
Things  must  be  arranged  by  their  resemblances  and  dif- 
ferences, (he  says  in  1750*,)  "but  the  resemblances  and 
differences  must  be  taken  not  from  one  part  but  from  the 
whole;  and   we  must  attend  to  the  form,  the  size,  the 
habit,  the  number  and  position  of  the  parts,  even  the 
substance  of  the  part ;  and  we  must  make  use  of  these 
elements  in  greater  or  smaller  number,  as  we  have  need." 
14.  Method  of  General  Comparison. — A  countryman 
of  Buffon,  who  shared  with  him   his  depreciating   esti- 
mate of  the   Linnsean  system,  and  his  wish  to  found  a 
natural  system  upon  a  broader  basis,  was  Adanson  ;    and 
he  invented  an  ingenious  method   of  apparently  avoid- 
ing the  vagueness  of  the  practice  of  following  the  general 
feeling  of  resemblance.     This  method  consisted  in  making 
many  artificial   systems,  in  each  of  which    plants  were 
arranged  by  some  one  part ;    and  then  collecting  those 
plants  which  came  near  each  other  in  the  greatest  number 
of  those  artificial  systems,  as  plants  naturally  the  most 
related.     Adanson  gives  an  account f  of  the  manner  in 
which  this  system  arose  in  his  mind.     He  had  gone  to 
Senegal,  animated  by  an  intense  zeal  for  natural  history; 
and  there,  amid  the  luxuriant  vegetation   of  the  torrid 
zone,  he  found  that  the  methods  of  Linnaeus  and  Tourne- 
fort  failed   him   altogether  as  means   of   arranging   his 
new  botanical  treasures.      He  was  driven  to  seek  a  new 

*  ADANSON,  p.  clvi.     BUFFON,  Hist.  Nat.,  t.  i.,  p.  21. 
t  Pref.,  p.  clvii. 

2  I  2 


484      PHILOSOPHY  OF  THE  CLASSIFICATORY  SCIENCES. 

system.  "  For  this  purpose,"  he  says,  "  I  examined 
plants  in  all  their  parts,  without  omitting  any,  from  the 
roots  to  the  embryo,  the  folding  of  the  leaves  in  the  bud, 
their  mode  of  sheathing*,  the  situation  and  folding  of 
the  embryo  and  of  its  radicle  in  the  seed,  relatively  to 
the  fruit;  in  short,  a  number  of  particulars  which  few 
botanists  notice.  I  made  in  the  first  place  a  complete 
description  of  each  plant,  putting  each  of  its  parts  in 
separate  articles,  in  all  its  details ;  when  new  species 
occurred  I  put  down  the  points  in  which  they  differed, 
omitting  those  in  which  they  agreed.  By  means  of  the 
aggregate  of  these  comparative  descriptions,  I  perceived 
that  plants  arranged  themselves  into  classes  or  families 
which  could  not  be  artificial  or  arbitrary,  not  being 
founded  upon  one  or  two  parts,  which  might  change  at 
certain  limits,  but  on  all  the  parts ;  so  that  the  dispropor- 
tion of  one  of  these  parts  was  corrected  and  balanced 
by  the  introduction  of  another."  Thus  the  principle  of 
resemblance  was  to  suffice  for  the  general  arrangement, 
not  by  means  of  a  new  principle,  as  symmetry  or  organi- 
zation, which  should  regulate  its  application,  but  by  a 
numeration  of  the  peculiarities  in  which  the  resemblance 
consisted. 

The  labour  which  Adanson  underwent  in  the  execu- 
tion of  this  thought  was  immense.  By  taking  each 
organ,  and  considering  its  situation,  figure,  number,  &c., 
he  framed  sixty-five  artificial  systems ;  and  collected  his 
natural  families  by  a  numerical  combination  of  these. 
For  example,  his  sixty-fifth  artificial  system  f  is  that  which 
depends  upon  the  situation  of  the  ovary  with  regard  to 
the  flower ;  according  to  this  system  he  frames  ten  artifi- 
cial classes,  including  ninety-three  sections :  and  of  these 
sections  the  resulting  natural  arrangement  retains  thirty- 
five,  above  one-third :  the  same  estimate  is  applied  in 
other  cases. 
*  "Lour  maniere  cle  sVngnincr."  t  ADANSON,  Prcf., p.  cccxii. 


METHODS  OF  NATURAL  HISTORY.  485 

But  this  attempt  to  make  number  supply  the  defects 
which  the  vague  notion  of  resemblance  introduces,  how- 
ever ingenious,  must  end  in  failure.  For,  as  Decan- 
dolle  observes  *,  it  supposes  that  we  know,  not  only  all  the 
organs  of  plants,  but  all  the  points  of  view  in  which  it  is 
possible  to  consider  them  ;  and  even  if  this  assumption 
were  true,  which  it  is,  and  long  must  be,  very  far  from 
being,  the  principle  is  altogether  vicious ;  for  it  supposes 
that  all  these  points  of  view,  and  all  the  resulting  artificial 
systems  are  of  equal  importance:  a  supposition  mani- 
festly erroneous.  We  are  thus  led  back  to  the  conside- 
ration of  the  relative  importance  of  organs  and  their 
qualities,  as  a  basis  for  the  classification  of  plants,  which 
no  artificial  method  can  supersede ;  and  thus  we  find  the 
necessity  of  attending  to  something  besides  mere  external 
and  detached  resemblance.  The  method  of  general  com- 
parison cannot,  any  more  than  the  method  of  blind  trial, 
lead  us,  with  any  certainty  or  clearness,  to  the  natural 
method.  Adanson's  families  are  held  by  the  best  botanists 
to  be,  for  the  greater  part  natural ;  but  his  hypotheses  are 
unfounded ;  and  his  success  is  probably  more  due  to  the 
dim  feeling  of  affinity,  by  which  he  was  unconsciously 
guided,  than  to  the  help  he  derived  from  his  numerical 
processes. 

15.  In  a  succeeding  chapter  I  shall  treat  of  that 
Natural  Affinity  on  which  a  Natural  System  must  really 
be  founded.  But  before  proceeding  to  this  higher  subject, 
we  must  say  a  few  words  on  some  of  the  other  parts  of 
the  philosophy  of  Natural  History, — the  Gradation  of 
Groups,  the  Nomenclature,  the  Diagnosis,  and  the  appli- 
cation of  the  methods  to  other  subjects. 

Gradation  of  Groups. — It  has  been  already  noticed 
(last  chapter,)  that  even  that  vague  application  of  the 
idea  of  resemblance  which  gives  rise  to  the  terms  of 

*  DEC.,  2%.JW.,p.67. 


486        PHILOSOPHY  OF  THE  CLASSIFICATORY  SCIENCES. 

common  language,  introduces  a  subordination  of  classes, 
as  man,  animal,  body,  substance.  Such  a  subordination 
appears  in  a  more  precise  form  when  we  employ  this 
idea  in  a  scientific  manner  as  we  do  in  Natural  History. 
We  have  then  a  series  of  divisions,  each  inclusive  of  the 
lower  ones,  which  are  expressed  by  various  metaphors  in 
different  writers.  Thus  some  have  gone  as  far  as  eight 
terms  of  the  series*,  and  have  taken,  for  the  most  part, 
military  names  for  them ;  as  Hosts,  Legions,  Phalanges, 
Centuries,  Cohorts,  Sections,  Genera,  Species.  But  the 
most  received  series  is  Classes,  Orders,  Genera,  and 
Species ;  in  which,  however,  we  often  have  other  terms 
interpolated,  as  Sub-genera,  or  Sections  of  genera.  The 
expressions  Family  and  Tribe,  are  commonly  appropriated 
to  natural  groups;  and  we  speak  of  the  Vegetable,  Ani- 
mal, Mineral  Kingdom ;  but  the  other  metaphors  of  Pro- 
vinces, Districts,  &c.,  which  this  suggests,  have  not 
been  commonly  used. 

It  will  of  course  be  understood  that  each  ascending 
step  of  classification  is  deduced  by  the  same  process  from 
the  one  below.  A  genus  is  a  collection  of  species  which 
resemble  each  other  more  than  they  resemble  other  spe- 
cies ;  an  order  is  a  collection  of  genera  having,  in  like 
manner,  the  first  degree  of  resemblance,  and  so  on. 
What  the  degrees  of  resemblance  are,  much  depend  upon 
the  nature  of  the  objects  compared,  and  cannot  possibly 
be  prescribed  before-hand.  Hence  the  same  term,  Class 
and  Order  for  instance,  may  imply  in  different  provinces 
of  nature  very  different  degrees  of  resemblance.  The 
Classes  of  Animals  are  Insects,  Birds,  Fish,  Beasts,  &c, 
The  Orders  of  Beasts  are  Ruminants,  Tardigrades,  Plan- 
tigrades, &c.  The  two  Classes  of  Plants  (according  to 
the  Natural  Orderf,)  are  Vascular  and  Cellular,  the 
latter  having  neither  sexes,  flowers,  nor  spiral  vessels. 
*  ADAKSON,  p.  cvi.  t  J  INDLEY, 


METHODS  OF  NATURAL  HISTORY.  487 

The  Vascular  Plants  are  divided  into  Orders,  as  Umlelli- 
fercs,  RanunculacecB,  &c.,  but  between  this  Class  and 
its  Orders  are  interposed  two  other  steps :  two  Sub- 
classes, Dicotyledonous  and  Monocotyledonous,  and  two 
Tribes  of  each  :  Angiospermi<e,  Gymnospermice  of  the 
first;  and  Petaloidece,  Glumacice  of  the  second.  Such 
interpolations  are  modifications  of  the  general  formula  of 
subordination  for  the  purpose  of  accommodating  it  to 
the  most  prominent  natural  affinities. 

16.  Species. — As  we  have  already  seen  in  tracing  the 
principles  of  the  natural  method,  when  by  the  intimate 
study  of  plants  we  seek  to  give  fixity  and  definiteness  to 
the  notion  of  resemblance  and  affinity  on  which  all  these 
divisions  depend,  we  are  led  to  the  study  of  organization 
and  analogy.  But  we  make  a  reference  to  physio- 
logical conditions  even  from  the  first,  with  regard  to  the 
lowest  step  of  our  arrangement,  the  species;  for  we 
consider  it  a  proof  of  the  impropriety  of  separating  two 
species,  if  it  be  shown  that  they  can  by  any  course  of 
propagation,  culture,  and  treatment,  the  one  pass  into 
the  other.  It  is  in  this  way,  for  example,  that  it  has 
been  supposed  to  be  established  that  the  common  prim- 
rose, oxlip,  polyanthus,  and  cowslip,  are  all  the  same 
species.  Plants  which  thus,  in  virtue  of  external  cir- 
cumstances, as  soil,  exposure,  climate,  exhibit  differences 
which  may  disappear  by  changing  the  circumstances, 
are  called  varieties  of  the  species.  And  thus  we  cannot 
say  that  a  species  is  a  collection  of  individuals  which 
possess  the  first  degree  of  resemblance ;  for  it  is  clear 
that  a  primrose  resembles  another  primrose  more  than  it 
does  a  cowslip  ;  but  this  resemblance  only  constitutes  a 
variety.  And  we  find  that  we  must  necessarily  include  in 
our  conception  of  species,  the  notion  of  propagation  from 
the  same  stock.  And  thus  a  species  has  been  well  de- 
fined*. "  The  collection  of  the  individuals  descended  from 
*  Cuv.,  Regne  Animal,  p.  19. 


488      PHILOSOPHY  OF  THE  CLASSIFICATORY  SCIENCES. 

one  another,  or  from  common  parents,  and  of  those  which 
resemble  these  as  much  as  these  resemble  each  other." 
And  thus  the  sexual  doctrine  of  plants,  or  rather  the 
consideration  of  them  as  things  which  propagate  their 
kind,  (whether  by  seed,  shoot,  or  in  any  other  way,)  is 
at  the  basis  of  our  classifications. 

17.  The  first  degree  of  resemblance  among  organized 
beings  is  thus  that  which  depends    on  this  relation  of 
generation,  and  we  might  expect  that  the  groups  which 
are  connected  by  this  relation  would  derive  their  names 
from  the  notion  of  generation.     It  is  curious  that  both  in 
Greek  and  Latin  languages  and  in  our  own,  the  words 
which  have  this  origin  (yevos,  genus,  kind)  do  not,  in  the 
phraseology  of  science  at  least,  denote  the  nearest  degree 
of  relationship,  but  have  other  terms  subordinate  to  them, 
which  appear  etymologically  to  indicate  a  mere  resem- 
blance of  appearance,  (elSos,  species,  sort,)   and  which  are 
appropriated  to  the  groups  resulting  from  propagation. 
Probably  the  reason  of  this  is,  that  the  former  terms  had 
been  applied  so  widely  and  loosely  before  the  scientific 
fixation  of  terms,  that  to  confine  them  to  what  we  call 
species  would  have  been  to  restrict  them  in  a  manner  too 
unusual  to  be  convenient. 

18.  Varieties.  Races. — The  Species,  as  we  have  said,  is 
the  collection  of  individuals  which  resemble  each  other  as 
much  as  do  the  offspring  of  a  common  stock.     But  within 
the  limits  of  this  boundary,  there  are  often  observable 
differences  permanent  enough  to  attract  our  notice,  though 
capable  of  being  obliterated  by  mixture  in  the  course  of 
generation.     Such   different  groups  are  called  Varieties. 
Thus  the  primrose  and  cowslip,  as  has  been  stated  above, 
are  found  to  be  varieties  of  the  same  plant ;   the  poodle 
and  the   greyhound   are  well   marked    varieties   of  the 
species  dog.     Such  differences  are  hereditary,  and  as  we 
have  seen,  it  may  be  long  doubtful  whether  such  here- 


METHODS  OF  NATURAL  HISTORY.  489 

ditary  differences  are  varieties  only,  or  different  species. 
In  such  cases  the  term  Race  has  been  applied. 

19.  (III.)  Nomenclature. — The  Nomenclature  of  any 
branch  of  Natural  History  is  the  collection  of  names  of  all 
its  species;  which,  when  they  become  extremely  numer- 
ous, requires  some  artifice  to  make  it  possible  to  recollect 
or  apply  them.  The  known  species  of  plants,  for  example, 
were  10,000  at  the  time  of  Linnoeus,  and  are  now  probably 
60,000.  It  would  be  useless  to  endeavour  to  frame  and 
employ  separate  names  for  each  of  these  species. 

The  division  of  the  objects  into  a  subordinated  system 
of  classification  enables  us  to  introduce  a  Nomenclature 
which  does  not  require  this  enormous  number  of  names. 
The  artifice  employed  to  avoid  this  inconvenience  is  to 
name  a  species  by  means  of  two  (or  it  might  be  more) 
steps  of  the  successive  division.  Thus  in  Botany  each  of 
the  genera  has  its  name,  and  the  species  are  marked  by 
the  addition  of  some  epithet  to  the  name  of  the  genus, 
In  this  manner  about  1,700  generic  names,  with  a  mo- 
derate number  of  specific  names,  were  found  by  Linnaeus 
sufficient  to  designate  with  precision  all  the  species  of 
vegetables  known  at  his  time.  And  this  Binary  Method 
of  Nomenclature  has  been  found  so  convenient  that  it 
has  been  universally  adopted  in  every  other  department 
of  the  Natural  History  of  organized  beings. 

Many  other  modes  of  Nomenclature  have  been  tried, 
but  no  other  has  at  all  taken  root.  Linna?us  himself 
appears  at  first  to  have  intended  marking  each  species  by 
the  generic  name  accompanied  by  a  characteristic  descrip- 
tive phrase;  and  to  have  proposed  the  employment  of  a 
trivial  specific  name,  as  he  termed  it,  only  as  a  method  of 
occasional  convenience.  The  use  of  these  trivial  names, 
has,  however,  become  universal,  as  we  have  said,  and  is 
by  many  persons  considered  •  the  greatest  improvement 
introduced  at  the  Linneean  reform. 


400        PHILOSOPHY  OF  THE  CLASSIFICATORY  SCIENCES. 

Both  Linnaeus  and  other  writers  (as  A  dan  son)  have 
given  many  maxims  with  a  view  of  regulating  the  selec- 
tion of  generic  and  specific  names.  The  maxims  of 
Linnaeus  were  intended  as  much  as  possible  to  exclude 
barbarism  and  confusion,  and  have,  upon  the  whole,  been 
generally  adopted ;  though  many  of  them  were  objected 
to  by  his  contemporaries  (Adanson  and  others*),  as 
capricious  or  unnecessary  innovations.  Many  of  the 
names,  introduced  by  Linnaeus,  certainly  appear  fanciful 
enough :  thus  he  gives  the  name  of  Bauhinia  to  a  plant 
with  leaves  in  pairs,  because  the  Bauhins  were  a  pair  of 
brothers  ;  Banisteria  is  the  name  of  a  climbing  plant,  in 
honour  of  Banister,  who  travelled  among  mountains. 
But  such  names,  once  established  by  adequate  authority, 
lose  all  their  inconvenience  and  easily  become  permanent ; 
and  hence  the  reasonableness  of  the  Linnaean.  rulef,  that 
as  such  a  perpetuation  of  the  names  of  persons  by  the 
names  of  plants  is  the  only  honour  botanists  have  to 
bestow,  it  ought  to  be  used  with  care  and  caution. 

The  generic  name  must,  as  Linnaeus  says,  be  fixed  \ 
before  we  attempt  to  form  a  specific  name  ;  "  the  latter 
without  the  former  is  like  the  clapper  without  the  bell." 
The  name  of  the  genus  being  established,  the  species  may 
be  marked  by  adding  to  it  "  a  single  word  taken  at  will 
from  any  quarter ;"  that  is,  not  involving  a  description  or 
any  essential  property  of  the  plant,  but  a  casual  or 
arbitrary  appellation.  Thus  the  various  species  of  Hiera- 
cium||  are  Hieradum  Alpinwn,  H.  Halleri,  H.  Pilosetta, 
H.  dubium,  H.  murorum,  &c.,  where  we  see  how  different 
may  be  the  kind  of  origin  of  the  words. 

Attempts  have  been  made  at  various  times  to  form 
the  names  of  species  from  those  of  genera  in  some  more 

*  Pp.  cxxix,  clxxii.  t  Phil.  Bot.,  Sec.  239. 

J  Ib.,  Sec.  222.          §  /$.,  Sec.  260. 

II  HOOKER,  Fl.  Scot.,  228. 


METHODS  OF  NATURAL  HISTORY.  491 

symmetrical  manner.  Thus  some  have  numbered  the 
species  of  genus  1,  2,  3,  &c.,  but  this  method  is  liable  to 
the  inconveniences,  first,  that  it  offers  nothing  for  the 
memory  to  take  hold  of;  and  second,  that  if  a  new 
species  intermediate  between  1  and  2,  2  and  3,  &c.,  be 
discovered,  it  cannot  be  put  in  its  place.  It  has  also 
been  proposed  to  mark  the  species  by  altering  the  termi- 
nation of  the  genus.  Thus  Adanson*,  denoting  a  genus 
by  the  name  Fonna  (Lyclmidea\  conceived  he  might 
mark  five  of  its  species  by  altering  the  last  vowel,  Fonna, 
Fonna-c,  Fonna-i,  Fonna-o,  Fonna-u;  then  others  by 
Fonna-ba,  Fonna-ka,  and  so  on.  This  course  would  be 
liable  to  the  same  evils  which  have  been  noticed  as 
belonging  to  the  numerical  method. 

The  names  of  plants  (and  the  same  is  true  of  animals) 
have  in  common  practice  been  binary  only,  consisting  of 
a  generic  and  a  specific  name.  The  Class  and  Order 
have  not  been  admitted  to  form  part  of  the  appellation  of 
the  species.  Indeed  it  is  easy  to  see  that  a  name  which 
must  be  identical  in  so  many  instances  as  that  of  an 
order  would  be,  would  be  felt  as  superfluous  and  burden- 
some. Accordingly,  Linnaeus  makes  it  a  preceptf,  that 
the  name  of  the  Class  and  the  Order  must  not  be  ex- 
pressed but  understood :  and  hence,  he  says,  Royen,  who 
took  Lilium  for  the  name  of  a  class,  rightly  rejected  it  as 
a  generic  name  and  substituted  Lirium,  with  the  Greek 
termination. 

Yet  we  must  not  too  peremptorily  assume  such 
maxims  as  these  to  be  universal  for  all  classificatory 
sciences.  It  is  very  possible  that  it  may  be  found 
advisable  to  use  three  terms,  that  of  order,  genus  and 
species,  in  designating  minerals,  as  is  done  in  Mohs's 
nomenclature ;  for  example,  Rhombohedral  Cole  Haloide, 
Paratomous  Hal  Baryte.  It  is  possible  also  that  it  may 

*  Pref.,  clxxvi.  f  Phil.  Bot.,  Sec.  215. 


492       PHILOSOPHY  OF  THE  CLASSIFICATORY  SCIENCES. 

be  found  useful  in  the  same  science  to  mark  some  of  the 
steps  of  classification  by  the  termination. 

Thus  it  has  been  proposed  to  confine  the  termination 
ite  to  the  Order  Silicides  of  Naumann,  as  Apophyllzfc, 
Stilbe'fc,  Leuczte,  &c.,  and  to  use  names  of  different  form 
in  other  orders,  as  Talc  Spar  for  Brennerite,  Pyramidal 
Titanium  Oxide  for  Octahedrite.  Some  such  method 
appears  to  be  the  most  likely  to  give  us  a  tolerable 
mineralogical  nomenclature. 

20.  (IV.)  Diagnosis. — German  Naturalists  speak  of  a 
part  of  the  general  method  which  they  call  the  Character- 
istic of  Natural  History,  and  which  is  distinguished  from 
the  Systematik  of  the  science.  The  Systematick  arranges 
the  objects  by  means  of  all  their  resemblances,  the  Cha- 
racteristick  enables  us  to  detect  their  place  in  the  arrange- 
ment by  means  of  a  few  of  their  characters.  What  these 
characters  are  to  be,  must  be  discovered  by  observation 
of  the  groups  and  divisions  of  the  system  when  they  are 
formed.  To  construct  a  collection  of  such  as  shall  be 
clear  and  fixed,  is  a  useful,  and  generally  a  difficult  task ; 
for  there  is  usually  no  apparent  connexion  between  the 
marks  which  are  used  in  discriminating  the  groups,  and 
the  nature  of  the  groups  themselves.  They  are  assumed 
only  because  the  Naturalist,  extensively  and  exactly 
acquainted  with  the  groups  and  the  properties  of  the 
objects  which  compose  them,  sees,  by  a  survey  of  the  field, 
that  these  marks  divide  it  properly. 

The  Characteristick  has  been  termed  by  some  English 
Botanists  the  Diagnosis  of  plants ;  a  word  which  we  may 
conveniently  adopt.  The  Diagnosis  of  any  genus  or 
species  is  different  according  to  the  system  we  follow. 
Thus  in  the  Linnoean  system  the  Diagnosis  of  the  Rose  is 
in  the  first  place  given  by  its  Class  and  Order:  it  is  Icosan- 
drous,  and  Polygynous ;  and  then  the  generic  distinction 
is  that  the  calyx  is  five-cleft,  the  tube  urceolate,  including 


METHODS  OF  NATURAL  HISTORY.  493 

many  hairy  aclienia,  the  receptacle  villous*.  In  the 
Natural  System  the  Rose-Tribe  are  distinguished  as 
beingf  "  Polypetalous  dicotyledons,  with  lateral  styles, 
superior  simple  ovaria,  regular  perigynous  stamens,  ex- 
albuminous  definite  seeds,  and  alternate  stipulate  leaves." 
And  the  true  Roses  are  further  distinguished  by  having 
"  Nuts,  numerous,  hairy,  terminated  by  the  persistent 
lateral  style  and  inclosed  within  the  fleshy  tube  of  the 
calyx,"  &c. 

It  will  be  observed  that  in  a  rigorous  artificial  system 
the  Systematick  coincides  with  the  C/iaractenstick ;  the 
Diataxis  with  the  Diagnosis ;  the  reason  why  a  plant  is 
put  in  a  division  is  identical  with  the  mode  by  which  it  is 
known  to  be  in  the  division.  The  Rose  is  in  the  class 
icosandria,  because  it  has  many  stamens  inserted  in  the 
calyx ;  and  when  we  see  such  a  set  of  stamens  we  imme- 
diately know  the  class.  But  this  is  not  the  case  with 
the  Diagnosis  of  natural  families.  Thus  the  genera  Za- 
mium  and  Galeopsis  (Dead  Nettle  and  Hemp  Nettle),  are 
each  formed  into  a  separate  group  in  virtue  of  their 
general  resemblances  and  differences,  and  not  because  the 
former  has  one  tooth  on  each  side  of  the  lower  lip,  and 
the  latter  a  notch  in  its  upper  lip,  though  they  are  dis- 
tinguished by  these  marks. 

Thus,  so  far  as  our  Systems  are  natural,  (which,  as  we 
have  shown,  all  systems  to  a  certain  extent  must  be),  the 
Characteristick  is  distinct  both  from  a  Natural  and  an 
Artificial  System ;  and  is,  in  fact,  an  Artificial  key  to  a 
Natural  System.  As  being  Artificial,  it  takes  as  few 
characters  as  possible ;  as  being  Natural,  its  characters 
are  not  selected  by  any  general  or  prescribed  rule,  but 
follow  the  natural  affinities.  The  Botanists  who  have 
made  any  steps  in  the  formation  of  a  natural  method  of 
plants  since  Linna3us,  have  all  attempted  to  give  a  Diag- 
nosis corresponding  to  the  Diataxis  of  their  method. 

*  LINDLEY,  Nat.  Syst.,  p.  J49.  t  /&.,  p.  81.  3. 


494 


CHAPTER  III. 

APPLICATION  OF  THE  NATURAL  HISTORY 
METHOD  TO  MINERALOGY. 

1.  THE  philosophy  of  the  Sciences  of  Classification  has 
had  great  light  thrown  upon  it  by  discussions  concerning 
the  methods  which  are  used  in  Botany :  for  that  science 
is  one  of  the  most  complete  examples  which  can  be  con- 
ceived of  the  consistent  and  successful  application  of  the 
principles  and  ideas  of  Classification ;  and  this  application 
has  been  made  in  general  without  giving  rise  to  any  very 
startling  paradoxes,  or  disclosing  any  insurmountable 
difficulties.  But  the  discussions  concerning  methods  of 
Mineralogical  Classification  have  been  instructive  for 
quite  a  different  reason :  they  have  brought  into  view  the 
boundaries  and  the  difficulties  of  the  process  of  Classifi- 
cation ;  and  have  presented  examples  in  which  every 
possible  mode  of  classifying  appeared  to  involve  inex- 
tricable contradictions.  I  will  notice  some  of  the  points 
of  this  kind  which  demand  our  attention,  referring  to  the 
works  published  recently  by  several  mineralogists. 

In  the  History  of  Mineralogy  we  noticed  the  attempt 
ipaade  by  Mohs  and  other  Germans  to  apply  to  minerals 
a  method  of  arrangement  similar  to  that  which  has  been 
so  successfully  employed  for  plants.  The  survey  which 
we  have  now  taken  of  the  grounds  of  that  method  will 
point  out  some  of  the  reasons  of  the  very  imperfect 
success  of  this  attempt.  We  have  already  said  that  the 
Terminology  of  Mineralogy  was  materially  reformed  by 
Werner,  and  including  in  this  branch  of  the  subject  (as 
we  must  do)  the  Crystallography  of  later  writers,  it  may 
be  considered  as  to  a  great  extent  complete.  Of  the 
attempts  at  a  Natural  arrangement,  that  of  Mohs  appears 


APPLICATION  TO  MINERALOGY.  495 

to  proceed  by  the  method  of  blind  trial,  the  undefinable 
perception  of  relationship  by  which  the  earliest  attempts 
at  a  Natural  Arrangement  of  plants  were  made.  Breit- 
haupt,  however,  has  made  (though  I  do  not  know  that  he 
has  published)  an  essay  in  a  mode  which  corresponds  very 
nearly  to  Adan son's  process  of  multiplied  comparisons. 
Having  ascertained  the  specific  gravity  and  hardness  of 
all  the  species  of  minerals,  he  arranged  them  in  a  table, 
representing  by  two  lines  at  right  angles  to  each  other 
these  two  numerical  quantities.  Thus  all  minerals  were 
distributed  according  to  two  co-ordinates  representing 
specific  gravity  and  hardness.  He  conceived  that  the 
groups  which  were  thus  brought  together  were  natural 
groups.  On  both  these  methods,  and  on  all  similar  ones, 
we  might  observe,  that  in  minerals  as  in  plants,  the  mere 
general  notion  of  likeness  cannot  lead  us  to  a  real  arrange- 
ment :  it  requires  to  have  precision  and  aim  given  it  by 
some  other  relation  ; — the  relation  of  chemical  composi- 
tion in  minerals,  as  the  relation  of  organic  function  in 
vegetables.  The  physical  and  crystallographical  properties 
of  minerals  must  be  studied  with  reference  to  their  con- 
stitution ;  and  they  must  be  arranged  into  groups  which 
have  some  common  chemical  character,  before  we  can 
consider  any  advance  as  made  towards  a  natural  arrange- 
ment. 

In  reality,  it  happens  in  Mineralogy  as  it  happened  in 
Botany,  that  those  speculators  are  regulated  by  an  obscure 
perception  of  this  ulterior  relation,  who  do  not  profess  to 
be  regulated  by  it.  Several  of  the  Orders  of  Mohs  have 
really  great  unity  of  chemical  character,  and  thus  have 
good  evidence  of  their  being  really  Natural  Orders. 

2.  Supposing  the  Diataxis  of  minerals  thus  obtained, 
Mohs  attempted  the  Diagnosis  ;  and  his  Characteristick  of 
the  Mineral  Kingdom,  published  at  Dresden,  in  1820,  was 
the  first  public  indication  of  his  having  constructed  a 


496         PHILOSOPHY  OF  THE  CLASSIPICATORY  SCIENCES. 

* 

system.  From  the  nature  of  a  Characteristic!*:,  it  is  neces- 
sarily brief,  and  without  any  ostensible  principle ;  but  its 
importance  was  duly  appreciated  by  the  author's  country- 
men. Since  that  time,  many  attempts  have  been  made 
at  improved  arrangements  of  minerals,  but  none,  I  think, 
(except  perhaps  that  of  Breithaupt,)  professing  to  pro- 
ceed rigorously  on  the  principles  of  Natural  History ; — to 
arrange  by  means  of  external  characters,  neglecting  alto- 
gether, or  rather  postponing,  the  consideration  of  chemical 
properties.  By  relaxing  from  this  rigour,  however,  and 
by  combining  physical  and  chemical  considerations, 
arrangements  have  been  obtained  (for  example,  that  of 
Naumann,)  which  appear  more  likely  than  the  one  of  Mohs 
to  be  approximations  to  an  ultimate  really  natural  system. 
Naumann's  Classes  are  Hydrolytes,  Hcdoides,  Silicides, 
Metal  Oxides,  Metals,  Sidphurides,  Anthracides,  with  sub- 
divisions of  Orders,  as  Anhydrous  wimetallic  Silicides. 
It  may  be  remarked  that  the  designations  of  these  are 
mostly  chemical.  As  we  have  observed  already,  che- 
mistry, and  mineralogy  in  its  largest  sense,  are  each  the 
necessary  supplement  of  the  other.  If  chemistry  furnish 
the  nomenclature,  mineralogy  must  supply  the  physio- 
graphy :  if  the  arrangement  be  founded  on  external 
characters,  and  the  names  independent  of  chemistry,  the 
chemical  composition  of  each  species  is  an  important 
scientific  truth  respecting  it. 

3.  The  inquiry  may  actually  occur,  whether  any  sub- 
ordination of  groups  in  the  mineral  kingdom  has  really 
been  made  out.  The  ancient  chemical  arrangements, 
for  instance,  that  of  Haiiy,  though  professing  to  distribute 
minerals  according  to  Classes,  Orders,  Genera,  and  Species, 
were  not  only  arbitrary,  but  inapplicable ;  for  the  first 
postulate  of  any  method,  that  the  species  should  have 
constant  characters  of  unity  and  difference,  was  not 
satisfied.  It  was  not  ascertained  that  carbonate  of  lime 


APPLICATION  TO  MINERALOGY.  497 

was  really  distinguishable  in  all  cases  from  carbonate  of 
magnesia,  or  of  iron ;  yet  these  species  were  placed  in  re- 
mote parts  of  the  system :  and  the  above  carbonates  made 
just  so  many  species,  although,  if  distinct  from  one  another 
at  all,  they  were  further  distinguishable  into  additional  spe- 
cies. Even  now,  we  may,  perhaps,  say  that  the  limits  of 
mineralogical  species,  and  their  laws  of  fixity,  are  not  yet 
clearly  seen.  For  the  discovery  of  the  isomorphous  rela- 
tions and  optical  properties  of  minerals  have  rather  shown 
us  in  what  direction  the  object  lies,  than  led  us  to  the  goal. 
It  is  clear  that,  in  the  mineral  kingdom,  the  Definition  of 
Species,  borrowed  from  the  laws  of  the  continuation  of 
the  kind,  which  holds  throughout  the  organic  world,  fails 
us  altogether,  and  must  be  replaced  by  some  other  con- 
dition :  nor  is  it  difficult  to  see  that  the  definite  atomic 
relations  of  the  chemical  constituents,  and  the  definite 
crystalline  angle,  must  supply  the  principles  of  the  specific 
identity  for  minerals.  Yet  the  exact  limits  for  the  defi- 
uiteness  in  both  these  cases  (when  we  admit  the  effect  of 
mechanical  mixtures,  &c.)  have  not  yet  been  completely 
disentangled.  It  is  clear  that  any  arbitrary  assumption 
(as  the  allowance  of  a  certain  per  centage  of  mixture,  or 
a  certain  small  deviation  in  the  angle,)  is  altogether  con- 
trary to  the  philosophy  of  the  natural  system,  and  can 
lead  to  no  stable  views.  It  is  only  by  laborious,  exten- 
sive, and  minute  research,  that  we  can  hope  to  attain  to 
any  solid  basis  of  arrangement. 

4.  Still,  though  there  are  many  doubts  respecting 
mineralogical  species,  a  large  number  of  such  species  are 
so  far  fixed  that  they  may  be  supposed  capable  of  being 
united  under  the  higher  divisions  of  a  system  with  approxi- 
mate truth.  Of  these  higher  divisions,  those  which  have 
been  termed  Orders  appear  to  tend  to  something  like  a 
fixed  chemical  character.  Thus  the  Haloids  of  Naumann, 
and  mostly  those  of  Mohs,are  combinations  of  an  oxide  with 
VOL.  i.  2  K 


498          PHILOSOPHY  OF  THE  CLASSIFICATORY  SCIENCES. 

an  acid,  and  thus  resemble  Salts,  whence  their  name.  The 
Silicides  contain  most  of  Mohs's  Spat/is:  and  the  Orders 
Pyrites,  Glance,  and  Blende,  are  common  to  Naumann 
and  Mohs  ;  being  established  by  the  latter  on  a  difference 
of  external  character,  which  difference  is,  indeed,  very 
manifest ;  and  being  included  by  the  former  in  one  che- 
mical Class,  Sulp/mrides.  The  distinctions  of  Hydrous 
and  Anhydrous,  Metallic  and  Unmetallic,  are,  of  course, 
chemical  distinctions,  but  occur  as  the  differences  of 
Orders  in  Naumann's  mixed  system. 

We  may  observe  that  some  French  writers,  following 
Haiiy's  last  edition,  use,  instead  of  metallic  and  unmetallic, 
autopside  metallic  and  heteropside  metallic;  meaning  by  this 
phraseology  to  acknowledge  the  discovery  that  earths,  &c., 
are  metallic,  though  they  do  not  appear  to  be  so,  while 
metals  both  are  and  appear  metallic.  But  this  seems  to 
be  a  refinement  not  only  useless  but  absurd.  For  what  is 
gained  by  adding  the  word  metallic,  which  is  common  to 
all,  and  therefore  makes  no  distinction  ?  If  certain  metals 
are  distinguished  by  their  appearing  to  be  metals,  this 
appearance  is  a  reason  for  giving  them  the  peculiar  name, 
metals.  Nothing  is  gained  by  first  bringing  earths  and 
metals  together,  and  then  immediately  separating  them 
again  by  new  and  inconvenient  names.  No  proposition 
can  be  expressed  better  by  calling  earths  heteropside  metal- 
lie  substances,  and  therefore  such  nomenclature  is  to  be 
rejected. 

Granting,  then,  that  the  Orders  of  the  best  recent  mine- 
ralogical  systems  approximate  to  natural  groups,  we  are  led 
to  ask  whether  the  same  can  be  said  of  the  Genera  of  the 
Natural  History  systems,  such  as  those  of  Mohs  and  Breit- 
haupt.  And  here  I  must  confess  that  I  see  no  principle 
in  these  genera,  and  have  failed  to  apprehend  the  concep- 
tions by  the  application  of  which  they  have  been  con- 
structed :  I  shall  therefore  not  pass  any  further  judgment 


APPLICATION  TO  MINERALOGY.  499 

upon  them.  The  subordination  of  Mineralogical  Species 
to  Orders  is  a  manifest  gain  to  science :  in  the  interposi- 
tion of  Genera  I  see  nothing  but  a  source  of  confusion. 

5.  In  Mineralogy,  as  in  other  branches  of  natural 
history,  a  reformed  arrangement  ought  to  give  rise  to  a 
reformed  Nomenclature ;  and  for  this,  there  is  more  occa- 
sion at  present  in  Mineralogy  than  there  was  in  Botany 
at  the  worst  period,  at  least  as  far  as  the  extent  of  the 
subject  allows.  The  characters  of  minerals  are  much 
more  dimly  and  unfrequently  developed  than*  those  of 
plants ;  hence  arbitrary  chemical  arrangements,  which 
could  not  lead  to  any  natural  groups,  and  therefore  not  to 
any  good  names,  prevailed  till  recently ;  and  this  state  of 
things  produced  an  anarchy  in  which  every  man  did  what 
seemed  right  in  his  own  eyes, — proposed  species  without 
any  ascertained  distinction,  and  without  a  thought  of 
subordination,  and  gave  them  arbitrary  names ;  and  thus 
with  only  about  two  or  three  hundred  known  species,  we 
have  thousands  upon  thousands  of  names,  of  anomalous 
form  and  uncertain  application. 

Mohs  has  attempted  to  reform  the  Nomenclature  of 
the  subject  in  a  mode  consistent  with  his  attempt  to 
reform  the  System.  In  doing  this,  he  has  fatally  trans- 
gressed a  rule  always  insisted  upon  by  the  legislators  of 
Botany,  of  altering  usual  names  as  little  as  possible ;  and 
his  names  are  both  so  novel  and  so  cumbrous,  that  they 
appear  to  have  little  chance  of  permanent  currency.  They 
are,  perhaps,  more  unwieldy  than  they  need  to  be,  by 
referring,  as  we  have  said,  to  three  of  the  steps  of  his 
classification,  the  Species,  Genus,  and  Order.  We  may, 
however,  assert  confidently,  from  the  whole  analogy  of 
natural  history,  that  no  good  names  can  be  found  which 
do  not  refer  to  at  least  two  terms  of  the  arrangement. 
This  rule  has  been  practically  adopted  to  a  great  extent 
by  Naumann,  who  gives  to  most  of  his  Haloids  the  name 

2  K  2 


500         PHILOSOPHY  OF  THE  CLASSIFICATOEY  SCIENCES. 

Spar,  as  Calc  spar,  Iron  spar,  &c.;  to  all  his  Oxides  the 
terminal  word  Erz  (Ore)',  and  to  the  species  of  the  orders 
Kies  (Pyrites),  Glance,  and  Blende,  these  names.  It  has 
also  been  theoretically  assented  to  by  Beudant,  who  pro- 
poses that  we  should  say  silicate  stilbite,  silicate  chabasie ; 
carbonate  calcaire,  carbonate  witherite ;  sulphate  couperose, 
&c.  One  great  difficulty  in  this  case  would  arise  from 
the  great  number  of  silicides ;  it  is  not  likely  that  any 
names  would  obtain  a  footing  which  tacked  the  term 
silicide  to  another  word  for  each  of  these  species.  The 
artifice  which  I  have  proposed,  in  order  to  obviate  this 
difficulty,  is  that  we  should  make  the  names  of  the  sili- 
cides, and  those  alone,  end  in  lie  or  lite,  which  a  large 
proportion  of  them  do  already. 

By  this  and  a  few  similar  contrivances,  we  might, 
I  conceive,  without  any  inconvenient  change,  introduce 
into  mineralogy  a  systematic  nomenclature. 

6.  I  shall  now  proceed  to  make  a  few  remarks  on  a 
work  on  mineralogy  more  recent  than  those  which  I  have 
above  noticed,  and  written  with  express  reference  to  such 
difficulties  as  I  have  been  discussing.  I  allude  to  the 
treatise  of  M.  Necker,  Le  Regne  Mineral  ramene  aux 
Methodes  d'HistoireNaturelle*,  which  also  contains  various 
dissertations  on  the  philosophy  of  classification  in  general, 
and  its  application  to  mineralogy  in  particular. 

M.  Necker  remarks  very  justly,  that  mineralogy,  as  it 
has  hitherto  been  treated,  differs  from  all  other  branches 
of  Natural  History  in  this  : — that  while  it  is  invested 
with  all  the  forms  of  the  sciences  of  classification, — 
Classes,  Divisions,  Genera,  and  the  like, — the  properties  of 
those  bodies  to  which  the  mineral ogical  student's  atten- 
tion is  directed  have  no  bearing  whatever  on  the  classi- 
fication. A  person,  he  remarks  f,  might  be  perfectly 
well  acquainted  with  all  the  characters  of  minerals  which 

*  Paris,  1835.  *  Regne  Mineral,  p.  3. 


APPLICATION   TO    MINERALOGY.  501 

Werner  or  Haiiy  examined  so  carefully,  and  might  yet  be 
quite  unable  to  assign  to  any  mineral  its  place  in  the 
divisions  of  their  methods.  There  is*  a  complete  sepa- 
ration between  the  study  of  mineralogical  characters  and 
the  recognition  of  the  name  and  systematic  place  of  a 
mineral.  Those  who  know  mineralogy  well,  may  know 
minerals  ill,  or  hardly  at  all ;  the  systematist  may  be  in 
such  knowledge  vastly  inferior  to  the  mineral-dealer  or 
the  miner.  In  this  respect  there  is  a  complete  contrast 
between  this  science  and  other  classificatory  sciences. 

Again,  in  the  best-known  systems  of  mineralogy,  (as 
those  of  Werner  and  Haiiy,)  the  bodies  which  are 
grouped  together  as  belonging  to  the  same  division,  have 
not,  as  they  have  in  other  classificatory  sciences,  any 
resemblance.  The  different  members  of  the  larger  classes 
are  united  by  the  common  possession  of  some  abstract 
property, — as,  that  they  all  contain  iron.  This  is  a  pro- 
perty to  which  no  common  circumstance  in  the  bodies 
themselves  corresponds.  What  is  there  common  to  the 
minerals  named  oxidulous  iron,  sulphuret  of  iron,  car- 
bonate of  iron,  sulphate  of  iron,  except  that  they  all 
contain  iron  ?  And  when  we  have  classed  these  bodies 
together,  what  general  assertion  can  we  make  concerning 
them,  except  that  which  is  the  ground  of  our  classifica- 
tion, that  they  contain  iron?  They  have  nothing  in 
common  with  iron  or  with  each  other  in  any  other  way.  ^ 

Again,  as  these  classes  have  no  general  properties,  all 
the  properties  are  particular  to  the  species ;  and  the 
descriptions  of  these  necessarily  become  both  tediously 
long,  and  inconveniently  insulated. 

7.  These  inconveniences  arise  from  making  chemical 
composition  the  basis  of  mineralogical  classification  with- 
out giving  chemical  analysis  the  first  place  among  mineral 
properties.     Shall  we,  then,  correct  this  omission,  so  far 
*  Regne  Mineral,  p.  8. 


502         PHILOSOPHY  OF  THE  CLASSIFICATORY  SCIENCES. 

as  it  has  affected  mineralogical  systems  ?  Shall  we  teach 
the  student  the  chemical  analysis  of  minerals,  and  then 
direct  him  to  classify  them  according  to  the  results  of  his 
analysis*? 

But  why  should  we  do  this  ?  To  what  purpose,  or  on 
what  ground,  do  we  arrange  the  results  of  chemical  ana- 
lysis according  to  the  forms  and  subordination  of  natural 
history  ?  Is  not  chemistry  a  science  distinct  from  natural 
history  ?  Are  not  the  sciences  opposed  ?  Is  not  natural 
history  confined  to  organic  bodies  ?  Can  mere  chemical 
elements  and  their  combinations  be,  with  any  propriety 
or  consistency,  arranged  into  species,  genera,  and  fami- 
lies ?  What  is  the  principle  on  which  genera  and  species 
depend?  Do  not  species  imply  individuals?  What  is 
an  individual  in  the  case  of  a  chemical  substance  ? 

8.  We  thus  find  some  of  the  widest  and  deepest 
questions  of  the  philosophy  of  classification  brought  under 
our  consideration  when  we  would  provide  a  method  for 
the  classification  of  minerals.  The  answers  to  these  ques- 
tions are  given  by  M.  Necker ;  and  I  shall  state  some  of 
his  opinions ;  taking  the  liberty  of  adding  such  remarks 
as  are  suggested  by  referring  the  subject  to  those  prin- 
ciples which  have  already  been  established  in  this  work. 

M.  Necker  asserts f  that  the  distinctions  of  different 
sciences  depend,  not  on  the  objects  they  consider,  but  on 
the  different  and  independent  points  of  view  on  which 
they  proceed.  Each  science  has  its  logic,  that  is,  its 
mode  of  applying  the  general  rules  of  human  reason  to 
its  own  special  case.  It  has  been  said  by  some^,  that  in 
minerals,  natural  history  and  chemistry  contemplate  com- 
mon objects,  and  thus  form  a  single  science.  But  do 
chemistry  and  natural  history  consider  minerals  in  the 
same  point  of  view? 

*  Regne  Mineral,  p.  18.  t  /£.,  p.  23. 

t  /ft.,  P-  27. 


APPLICATION  TO  MINERALOGY.  503 

The  answer  is,  that  they  do  not.  Physics  and  che- 
mistry consider  the  properties  of  bodies  in  an  abstract 
manner ;  as,  their  composition,  their  elements,  their  mu-* 
tual  actions,  with  the  laws  of  these ;  their  forces,  as 
attraction,  affinity;  all  which  objects  are  abstract  ideas. 
In  these  cases  we  have  nothing  to  do  with  bodies  them* 
selves,  but  as  the  vehicles  of  the  powers  and  properties 
which  we  contemplate. 

-  Natural  history,  on  the  other  hand,  has  to  do  with 
natural  bodies :  their  properties  are  not  considered  ab^ 
stractedly,  but  only  as  characters.  If  the  properties  are 
abstracted,  it  is  but  for  a  moment.  Natural  history  has  to 
describe  and  class  bodies  as  they  are.  All  which  cannot 
be  perceived  by  the  senses,  belongs  not  to  its  domain,  as 
molecules,  atoms,  elements. 

Natural  history*  may  have  recourse  to  physics  or 
chemistry  in  order  to  recognise  those  properties  of  bodies 
which  serve  as  characters ;  but  natural  history  is  not,  on 
that  account,  physics  or  chemistry.  Classification  is  the 
essential  business  of  the  natural  historianf,  to  which 
task  chemistry  and  physics  are  only  instrumental,  and 
the  further  account  of  properties  only  complementary. 

It  has  been  said,  in  support  of  the  doctrine  that 
chemistry  and  mineralogy  are  identical,  that  chemistry 
does  not  neglect  external  characters.  "  The  chemist  in 
describing  sulphur,  mentions  its  colour,  taste,  odour,  hard"- 
ness,  transparence,  crystalline  form,  specific  gravity ;  how- 
does  he  then  differ  from  the  mineralogist  ?"  But  to  this 
it  is  replied,  that  these  notices  of  the  external  characters 
of  this  or  any  substance  are  introduced  in  chemistry 
merely  as  convenient  marks  of  recognition  ;  whereas  they 
are  essential  in  mineralogy.  If  we  had  taken  the  account 
given  of  several  substances  instead  of  one,  we  should 
have  seen  that  the  chemist  and  the  naturalist  consider 

*  Reyne  Mineral,  p.  37.  t  /&.,  p.  41. 


304      PHILOSOPHY  OF  THE  CLASSIFICATORY  SCIENCES. 

them  in  ways  altogether  different.  The  chemist  will 
make  it  his  business  to  discover  the  mutual  action  of  the 
substances ;  he  will  combine  them,  form  new  products, 
determine  the  proportions  of  the  elements.  The  minera- 
logist will  divide  the  substances  into  groups  according 
to  their  properties,  and  then  subdivide  these  groups,  till  he 
refers  each  substance  to  its  species.  Exterior  and  phy- 
sical characters  are  merely  accessory  and  subordinate  for 
the  chemist;  chemistry  is  merely  instrumental  for  the 
mineralogist. 

This  view  agrees  with  that  to  which  we  have  been  led 
by  our  previous  reasonings;  and  may,  according  to  our  prin- 
ciples, be  expressed  briefly  by  saying,  that  the  Idea  which 
chemistry  has  to  apply  is  the  idea  of  Elementary  Composi- 
tion, while  natural  history  applies  the  Idea  of  graduated 
Resemblances,  and  thus  performs  the  task  of  classification. 

9.  The  question  occurs*,  whether  Natural  History 
can  be  applied  to  Inorganic  Substances  ?  And  the  answer 
to  this  question  is,  that  it  can  be  applied,  if  there  are 
such  things  as  inorganic  individuals,  since  the  resem- 
blances and  differences  with  which  natural  history  has  to 
do  are  the  resemblances  and  differences  of  individuals. 

What  is  an  Individual  ?  It  certainly  is  not  that 
which  is  so  simple  that  it  cannot  be  divided.  Individual 
animals  are  composed  of  many  parts.  But  if  we  exa- 
mine, we  shall  find  that  our  idea  of  an  individual  is,  that 
it  is  a  whole  composed  of  parts,  which  are  not  similar  to 
the  whole,  and  have  not  an  independent  existence,  while 
the  whole  has  an  independent  existence  and  a  definite 
form  f. 

What  then  is  the  Mineralogical  Individual  ?  At  first, 
while  minerals  were  studied  for  their  use,  the  most  pre- 
cious of  the  substances  which  they  contained  was  looked 
upon  as  the  characteristic  of  the  mineral.  The  smallest 

*  Regne  Mineral t  p.  46.  t  ./&.,  p.  52. 


APPLICATION  TO  MINERALOGY.  505 

trace  of  silver  made  a  mineral  an  ore  of  silver.  Thus 
forms  and  properties  were  disregarded,  and  substance  was 
considered  as  identical  with  mineral.  And  hence*  Dau- 
benton  refused  to  recognise  species  in  the  mineral  king- 
dom, because  he  recognised  no  individuals.  He  proposed 
to  call  sorts  what  we  call  species.  In  this  way  of  con- 
sidering minerals,  there  are  no  individuals. 

10.  But  still  this  is  not  satisfactory:  for  if  we  take  a  well 
formed  and  distinct  crystal,  this  clearly  is  an  individual! . 

It  may  be  objected,  that  the  crystal  is  divisible  (ac- 
cording to  the  theory  of  crystallography)  into  smaller 
solids ;  that  these  small  solids  are  really  the  simple  ob- 
jects ;  and  that  actual  crystals  are  formed  by  combinations 
of  these  molecules  according  to  certain  laws. 

But,  as  we  have  already  said,  an  individual  is  sflch, 
not  because  it  cannot  be  divided,  but  because  it  cannot 
be  divided  into  parts  similar  to  the  whole.  As  to  the 
division  of  the  form  into  its  component  laws,  this  is  an 
abstract  proceeding,  foreign  to  natural  history i:.  There- 
fore there  is  so  far  nothing  to  prevent  a  crystal  from  being 
an  individual. 

11.  We  cannot  (M.  Necker  goes  on  to  remark)  con- 
sider the  Integrant  Molecules  as  individuals.     These  are 
useful  abstractions,  but  abstractions  only,  which  w£  must 
not  deal  with  as  real  objects.     Haiiy  himself  warns  us  § 
that  his  doctrine  of  increments  is  a  purely  abstract  con- 
ception,   and    that   nature,    in  fact,  follows   a   different 
process.      Accordingly,   Weiss  and  Mohs  express  laws 
identical  with  those  of  Haiiy,  without  even  speaking  of 
molecules;   and  Wollaston  and  Davy  have  deemed  it 
probable   that  the  molecules  are  not  polyhedrons,  but 
spheres  or  spheroids.     Such  mere  creations  of  the  mind 
can  never  be  treated  as  individuals.     If  the  maxim  of 

*  Rtyne  Mineral,  p.  54.  t  Ib.,  p.  56.          4  Ib.y  p.  58. 

§A,  p.  61. 


506        PHILOSOPHY  OF  THE  CLASSIFICATORY  SCIENCES. 

natural  history,  that  the  species  is  a  collection  of  indi- 
viduals, be  applied  so  as  to  make  those  individuals  mere 
abstractions ;  or  if,  instead  of  individuals,  we  take  such 
an  abstraction  as  substance  or  matter,  the  course  of  natu- 
ral history  is  altogether  violated.  And  yet  this  error  has 
hitherto  generally  prevailed ;  and  mineralogists  have  clas- 
sified, not  things,  but  abstract  ideas*. 

.12.  But  it  may  be  saiclf,  will  not  the  small  solids  obtained 
by  Cleavage  better  answer  the  idea  of  individuals?  To 
this  it  is  replied,  that  these  small  solids  have  no  indepen- 
dent existence.  They  are  only  the  result  of  a  mode  of 
division.  They  are  never  found  separate  and  indepen- 
dent. The  secondary  forms  which  they  compose  are 
determined  by  various  circumstances  (the  nature  of  the 
solution,  &c.),  and  the  cleavage  which  produces  these 
small^  solids  is  only  one  result  among  many  from  the  crys- 
talline forces $. 

Thus  neither  integrant  molecules,  nor  solids  obtained 
by  cleavage,  can  be  such  mineral ogical  individuals  as  the 
spirit  of  natural  history  requires.  Hence  it  appears  that 
we  must  take  the  real  crystals  for  individuals  $. 

13.  We    must,    however,    reject    crystals    (generally 
large  ones)  which  are  obviously  formed  of  several  smaller 
ones  of  a  similar  form  (as  occurs  so  often  in  quartz  and 
calc  spar).     We  must  also  distinguish  cases  in  which  a 
large  regular  form  is  composed  of  smaller  but  different 
regular  forms  (as  octahedrons  of  fluor  spar  made  up  of 
cubes).     Here  the  small  component  forms  are  the  indi- 
viduals.    Also  we  must  notice  the  cases  ||  in  which  we 
have  a  natural  crystal,  similar  to  the  primary  form.    Here 
the  face  will  show  whether  the  body  is  a  result  obtained 
by  cleavage  or  a  natural  individual. 

14.  It  will  be  objected^!,  that  the  crystalline  form  ought 

*  Regne  Mineral,  p.  67-  t  Ib.,  p.  69.  J  Ib.,  p.  71. 

§  Ib.,  p.  73.  ||  Ib.t  p.  75.  1T  Ib.,  p.  79. 


APPLICATION  TO  MINERALOGY.  507 

not  to  be  made  the  dominant  character  in  mineralogy, 
since  it  rarely  occurs  perfect.  To  this  it  is  replied,  that 
even  if  the  application  of  the  principle  be  difficult,  still  it 
has  been  shown  to  be  the  only  true  principle,  and  there- 
fore we  have  no  alternative.  But  further*,  it  is  not  true 
that  amorphous  substances  are  more  numerous  than  crys- 
tals. In  LEONHARD'S  Manual  of  Oryctoynosy,  there  are 
377  mineral  substances.  Of  these,  281  have  a  crystalline 
structure,  and  96  only  have  not  been  found  in  a  regular 
form. 

Again,  the  281  crystalline  forms  have  each  its  varie- 
ties, some  of  which  are  crystalline,  and  some  are  not  so. 
Now  the  crystalline  varieties  amount  to  1453,  and  the 
uncrystalline  to  180  only.  Thus  mineralogy,  according 
to  the  view  of  it  here  presented,  has  a  sufficiently  wide, 
fieldf. 

15.  It  will  be  objected \>  that  according  to  this  mode 
of  proceeding,  we  must  reject  from  our  system  all  non- 
crystalline  minerals.  But  we  reply,  that  if  the  mass  be 
composed  of  crystals,  the  size  of  the  crystals  makes  no 
difference.  Now  lamellar  and  other  compact  masses  are 
very  generally  groups  of  crystals  in  various  positions. 
Individuals  mutilated  and  mixed  together  are  not  the  less 
individuals ;  and  therefore  such  masses  may  be  treated  as 
objects  of  natural  history. 

If  we  cannot  refer  all  rocks  to  crystalline  species,^ 
those  which  elude  our  method  may  appear  as  an  appen- 
dix, corresponding  to  those  which  botanists  call  genera 
incertce  sedis§. 

But  these  genera  and  species  will  often  be  afterwards 
removed  into  the  crystalline  part  of  the  system,  by  being 
identified  with  crystalline  species.  Thus  pyrope,  &c., 
have  been  referred  to  garnet,  and  basalt,  wacke,  &c.,  to 

*  Regne  Mineral,  p.  82.          t  /&.,  p.  85.          J  Ib.t  p.  86. 
§/6.,.  91., 


508         PHILOSOPHY  OF  THE  CLASSIFICATORY  SCIENCES. 

compound  rocks.  Thus  veins  of  dolerite,  visibly  com- 
posed of  two  or  three  elements,  pass  to  an  apparently 
simple  state  by  becoming  fine-grained*. 

16.  Finally f,  we  have  to  ask,  are  artificial  crystals  to 
enter  into  our  classification?     M.  Necker  answers,  No; 
because  they  are  the  result  of  art,  like  mules,  mestizos, 
hybrids,  and  the  like. 

17.  Upon  these  opinions,  we  may  observe,  that  they 
appear  to  be,  in  the  main,  consistent  with  the  soundest 
philosophy.     That  each  natural  crystal  is  an  individual, 
is  a  doctrine  which  is  the  only  basis  of  mineralogy  as  a 
Natural  Historical  science;    yet  the   imperfections  and 
confused  unions  of  crystals  make  this  principle  difficult 
to  apply.     Perhaps  it  may  be  expressed  in  a  more  precise 
manner  by  referring  to  the  crystalline  forces,  and  to  the 
axes  by  which  their  operation  is  determined,  rather  than 
to  the  external  form.     That  portion  of  a  mineral  sub- 
stance is  a  mineralogical  individual  which  is  determined 
by  crystalline  forces  acting  to  the  same  axes.     In  this 
way  we  avoid  the  difficulty  arising  from  the  absence  of 
faces,  and  enable  ourselves  to  use  either  cleavage,  or  optical 
properties,  or  any  others,  as  indications  of  the  identity  of 
the  individual.    The  individual  extends  so  far  as  the  polar 
forces  extend  by  which  crystalline  form  is  determined, 
whether  or  not  those  forces  produce  their  full  effect,  a 
perfectly  circumscribed  polyhedron. 

18.  There  is  only  one  material  point  on  which  our 
principles  lead  us  to  differ  from  M.  Necker ; — the  pro- 
priety of  including  artificial  crystals  in  our  mineralogical 
classification.     To  exclude  them,  as  he  does,  is  a  conclu- 
sion so  entirely  at  variance  with  the  whole  course  of  his 
own  reasonings,  that  it  is  difficult  to  conceive  that  he  would 
persist  in  his  conclusion,  if  his  attention  were  drawn  to 
the  question  more  steadily.     For,  as  he  justly  sayst,  each 

*  Regne  Mineral,  p.  93.  t  /£.,  p.  95.  J  Ib.t  p.  23. 


APPLICATION  TO  MINERALOGY.  509 

science  has  its  appropriate  domain,  determined  by  its 
peculiar  point  of  view.  Now  artificial  and  natural  crys- 
tals are  considered  in  the  same  point  of  view,  (namely, 
with  reference  to  crystalline,  physical,  and  optical  pro- 
perties, as  subservient  to  classification,)  and  ought,  there- 
fore, to  belong  to  the  same  science.  Again,  he  says*, 
that  chemistry  would  reject  as  useless  all  notice  of  the 
physical  properties  and  external  characters  of  substances,  if 
a  special  science  were  to  take  charge  of  the  description  and 
classification  of  these  products.  But  such  a  special  science 
must  be  mineralogy ;  for  we  cannot  well  make  one  science 
of  classification  of  natural,  and  another  of  artificial  sub- 
stances :  or  if  we  do,  the  two  sciences  will  be  identical 
in  method  and  principles,  and  will  extend  over  each 
other's  boundaries,  so  that  it  will  be  neither  useful  nor 
possible  to  distinguish  them.  Again,  M.  Necker's  own 
reasonings  on  the  selection  of  the  individual  in  minera- 
logy are  supported  by  well  chosen  exarnplesf ;  but  these 
examples  are  taken  from  artificial  salts ;  as,  for  instance, 
common  salt  crystallizing  in  different  mixtures.  Again, 
the  analogy  of  mules  and  mestizos,  as  products  of  art, 
with  chemical  compounds,  is  not  just.  Chemical  com- 
pounds correspond  rather  to  natural  species,  propagated 
by  man  under  the  most  natural  circumstances,  in  order 
that  he  may  study  the  laws  of  their  production^. 

19.  But  the  decisive  argument  against  the  separation 
of  natural  and  artificial  crystals  in  our  schemes  of  classi- 
fication is,  that  we  cannot  make  such  a  separation.  Sub- 
stances which  were  long  known  only  as  the  products  of 
the  laboratory,  are  often  discovered,  after  a  time,  in 
natural  deposits.  Are  the  crystals  which  are  found  in  a 
forgotten  retort  or  solution  to  be  considered  as  belonging 

*  Regne  Mineral,  p.  36.  t  Ib.,  p.  71. 

J  We  may  remark  that  M.  Necker,  in  his  own  arrangement  of 
minerals,  inserts  among  his  species  iron  and  lead,  which  do  not  occur 
native. 


510         PHILOSOPHY  OF  THE  CLASSIFICATORY  SCIENCES. 

to  a  different  science  from  those  which  occur  in  a  deserted 
mine  ?  And  are  the  crystals  which  are  produced  where 
man  has  turned  a  stream  of  water  or  air  out  of  its  course, 
to  be  separated  from  natural  crystals,  when  the  composi- 
tion, growth,  and  properties,  are  exactly  the  same  in 
both  ?  And  again  :  How  many  natural  crystals  can  we 
already  produce  by  synthesis  !  How  many  more  may  we 
hope  to  imitate  hereafter !  M.  Necker  himself  states*, 
that  Mitscherlich  found,  in  the  scoriae  of  the  mines  of 
Sweden  and  Germany,  artificial  minerals  having  the  same 
composition  and  the  same  crystalline  form  with  natural 
minerals :  as  silicates  of  iron,  lime,  and  magnesia  agree- 
ing with  peridot ;  bisilicate  of  iron,  lime,  and  magnesia 
agreeing  with  pyroxene ;  red  oxide  of  copper ;  oxide  of 
zinc  ;  protoxide  of  iron  (fer  bxydule);  sulphurets  of  iron, 
zinc,  lead ;  arseniuret  of  nickel ;  black  mica.  These 
were  accidental  results  of  fusion.  But  M.  Berthier,  by 
bringing  together  the  elements  in  proper  quantities,  has 
succeeded  in  composing  similar  minerals,  and  has  thus 
obtained  artificial  silicates,  with  the  same  forms  and  the 
same  characters  as  natural  silicates.  Other  chemists 
(M.  Haldat,  M.  Becquerel)  have,  in  like  manner,  obtained, 
by  artificial  processes,  other  crystals,  known  previously 
as  occurring  naturally.  How  are  these  crystals,  thus 
identical  with  natural  minerals,  to  be  removed  out  of  the 
domain  of  mineralogy,  and  transferred  to  a  science  which 
shall  classify  artificial  crystals  only?  If  this  be  done,  the 
mineralogist  will  not  be  able  to  classify  any  specimen  till 
he  has  human  testimony  whether  it  was  found  naturally 
occurring  or  produced  by  chemical  art.  Or  is  the  other 
alternative  to  be  taken,  and  are  these  crystals  to  be  given 
up  to  mineralogy  because  they  occur  naturally  also? 
But  what  can  be  more  unphilosophical  than  to  refer  to 
separate  sciences  the  results  of  chemical  processes  closely 

*  Regrie  Mineral,  p.  151. 


APPLICATION  TO  MINERALOGY. 


511 


allied,  and  all  but  identical?  The  chemist  constructs 
bisilicates,  and  these  are  classified  by  the  mineralogist : 
but  if  he  constructs  a  trisilicate,  it  belongs  to  anotlier 
science.  All  these  intolerable  incongruities  are  avoided 
by  acknowledging  that  artificial,  as  well  as  natural, 
crystals  belong  to  the  domain  of  mineralogy.  It  is,  in 
fact,  the  name  only  of  mineralogy  which  appears  to  dis- 
cover any  inconsistency  in  this  mode  of  proceeding. 
Mineralogy  is  the  representative  of  a  science  which  has 
a  wider  office  than  mineralogists  first  contemplated ;  but 
which  must  exist,  in  order  that  the  body  of  science  may 
be  complete.  There  must,  as  we  have  already  said,  be  a 
Science,  the  object  of  which  is  to  classify  bodies  by  their 
physical  characters,  in  order  that  we  may  have  some 
means  of  asserting  chemical  truths  concerning  bodies; 
some  language  in  which  we  may  express  the  propositions 
which  chemical  analysis  discovers.  And  this  Science  will 
have  its  object  prescribed,  not  by  any  accidental  or  arbitrary 
difference  of  the  story  belonging  to  each  specimen ;— not 
by  knowing  whether  the  specimen  was  found  in  the 
mine  or  in  the  laboratory;  produced  by  attempting  to 
imitate  nature,  or  to  do  violence  to  her : — but  will  have 
its  course  determined  by  its  own  character.  The  range 
and  boundaries  of  this  Science  will  be  regulated  by  the 
ideas  with  which  it  deals.  Like  all  *  other  sciences,  it 
must  extend  to  everything  to  which  its  principles  apply. 
The  limits  of  the  province  which  it  includes  are  fixed 
by  the  consideration  that  it  must  be  a  connected  whole. 
No  previous  definition,  no  historical  accident,  no  casual 
phrase,  can  at  all  stand  in  the  way  of  philosophical  coii!- 
sistency; — can  make  this  Science  exclude  what  that 
includes,  or  oblige  it  to  admit  what  that  rejects.  And  thus, 
whatever  we  call  our  Science; — whether  we  term  it 
External  Chemistry,  Mineralogy,  the  Natural  History  of 
Inorganic  Bodies ; — since  it  can  be  nothing  but  the 


PHILOSOPHY  OF  THE  CLASSIFICATORY  SCIENCES. 

Science  of  the  Classification  of  Inorganic  Bodies  of  definite 
forms  and  properties,  it  must  classify  all  such  bodies, 
whether  or  not  they  be  minerals,  and  whether  or  not  they 
be  natural. 

20.  In  the  application  of  the  principles  of  classifica- 
tion to  minerals,  the  question  occurs,  What  are  to  be 
considered  as  mineral  Species?  By  Species  we  are  to 
understand,  according  to  the  usage  of  other  parts  of 
natural  history,  the  lowest  step  of  our  subordinate  divi- 
sions ; — the  most  limited  of  the  groups  which  have  defi- 
nite distinctions.  What  definite  distinctions  of  groups 
of  objects  of  any  kind  really  occur  in  nature,  is  to  be 
learnt  from  an  examination  of  nature :  and  the  result  of 
our  inquiries  will  be  some  general  principle  which  con- 
nects the  members  of  each  group,  and  distinguishes  the 
members  of  groups  which,  though  contiguous,  are  dif- 
ferent In  the  classification  of  organized  bodies,  the  rule 
which  thus  presides  over  the  formation  of  Species  is  the 
principle  of  reproduction.  Those  animals  and  those 
plants  are  of  the  same  Species  which  are  produced  from 
a  common  stock,  or  which  resemble  each  other  as  much 
as  the  progeny  of  a  common  stock.  Accordingly  in 
practice,  if  any  questions  arise  whether  two  varieties  of 
form  be  of  the  same  or  different  species,  it  is  settled  by 
reference  to  the  fact  of  reproduction;  and  when  it  is 
ascertained  that  the  two  forms  come  within  the  habitual 
and  regalar  limits  of  a  common  circle  of  reproduction, 
they  are  held  to  be  of  the  same  species.  Now  in  crystals, 
this  principle  of  reproduction  disappears  altogether,  and 
the  basis  of  the  formation  of  species  must  be  sought 
elsewhere.  We  must  have  some  other  principle  to 
replace  the  reproduction  which  belongs  only  to  organic 
life.  This  principle  will  be,  we  may  expect,  one  which 
secures  the  permanence  and  regularity  of  mineral  forms, 
as  tke  reproductive  power  does  of  animal  and  vegetable. 


APPLICATION  TO  MINERALOGY.  513 

Such  a  principle  is  the  Power  of  Crystallization.  The 
forces  of  which  solidity,  cohesion,  and  crystallization  are 
the  result,  are  those  which  give  to  minerals  their  perma- 
nent existence  and  their  physical  properties;  and  ever 
since  the  discovery  of  the  distinctions  of  crystalline  forms 
and  crystalline  systems,  it  is  certain  that  this  force  dis- 
tinguishes groups  of  crystals  in  the  most  precise  and 
definite  manner.  The  rhombohedral  carbonates  of  lime 
and  of  iron,  for  instance,  are  distinguished  exactly  by  the 
angles  of  their  rhombohedrons.  And  if,  in  the  case  of 
any  proposed  crystal,  we  should  doubt  to  which  kind  the 
specimen  belongs,  the  measurement  of  the  angles  of 
cleavage  would  at  once  decide  the  question.  The  prin- 
ciple of  crystallization  therefore  appears,  from  analogy, 
to  be  exactly  fitted  to  take  the  place  of  the  principle  of 
animal  generation.  The  forces  which  make  the  indivi- 
dual permanent  and  its  properties  definite,  here  stand  in 
the  place  of  the  forces  which  preserve  the  race,  while 
individuals  are  generated  and  die. 

21.  According  to  this  view,  the  different  modifica- 
tions of  the  same  crystalline  form  would  be  Varieties  only 
of  the  same  species.  All  the  various  solids,  for  example, 
which  are  produced  by  the  different  laws  of  derivation  of 
rhombohedral  carbonate  of  lime,  would  fall  within  the 
same  Species.  And  this  appears  to  be  required  by  the 
general  analogy  of  natural  history.  For  these  differences 
of  form,  produced  by  the  laws  of  crystalline  deriva- 
tion, are  not  definite.  The  faces  which  are  added  to 
one  form  in  order  to  produce  another,  may  be  of  any 
size,  small  or  large,  and  thus  the  crystal  which  represents 
one  modification  passes  by  insensible  degrees  to  another. 
The  forms  of  calc  spar,  which  we  call  dog-tooth  spar, 
cannon  spar,  nail-head  spar,  and  the  like,  appear  at  first, 
no  doubt,  distinct  enough ;  but  so  do  the  races  of  dogs. 
And  we  find,  in  the  mineral  as  in  the  animal,  that  the 
VOL.  i.  2  L 


514         PHILOSOPHY  OF  THE  CLASSIFICATORY  SCIENCES. 

distinction  is  obliterated  by  taking  such  intermediate 
steps  as  really  occur.  And  if  a  fragment  of  any  of  these 
crystals  is  given  us,  we  can  determine  that  it  is  rhombo- 
hedral  carbonate  of  lime ;  but  it  is  not  possible,  in 
genera],  to  determine  to  which  of  the  kinds  of  crystal  it 
has  belonged. 

22.  Notwithstanding  these  considerations,  M.  Necker 
has  taken  for  his  basis  of  mineral  species*  the  Secondary 
Modifications,  and  not  the  Primary  Forms.  Thus  cubical 
galena,  octahedral  galena,  and  triform  galena,  are,  with  him, 
three  species  of  crystals. 

On  this  I  have  to  observe,  as  I  have  already  done, 
that  on  this  principle  we  have  no  definite  distinction  of 
species ;  for  these  forms  may  and  do  pass  into  each 
other:  among  cubo-octahedrons  of  galena  occur  cubes 
and  octahedrons,  as  one  face  or  another  vanishes,  and 
the  transition  is  insensible.  We  shall,  on  this  principle, 
find  almost  always  three  or  four  species  in  the  same  tuft 
of  crystals ;  for  almost  every  individual  in  such  assem- 
blages may  exhibit  a  different  combination  of  secondary 
faces.  Again,  in  cases  where  the  secondary  laws  are 
numerous,  it  would  be  impracticable  to  enumerate  all 
their  combinations,  and  impossible  therefore  to  give  a 
list  of  species.  Accordingly  M.  Neckerf  gives  seventy- 
one  Species  of  spath  calcaire,  and  then  says,  "  Nous 
n'avons  pas  enumere  la  dixieme  partie  des  especes  con- 
nues  de  ce  genre,  qui  se  m  on  tent  a  plus  de  huit  cents." 
Again,  in  many  substances,  of  which  few  crystals  are 
found,  every  new  specimen  would  be  a  new  species ;  if 
indeed  it  were  perfect  enough  to  be  referred  to  a  species 
at  all.  But  from  a  specimen  without  perfect  external 
form,  however  perfect  in  crystalline  character,  although 
everything  else  might  be  known, — angles,  optical  pro- 

*  Regne  Mineral,  p.  396,  t  Ib.  ii.  634. 


APPLICATION  TO  MINERALOGY.  515 

perties,  physical  properties,  and  chemical  constitution, — 
the  species  could  not  be  determined.  Thus  Necker  says* 
of  the  micas,  "  Quant  aux  especes  propre  a  chaque  genre, 
la  lac une  sera  presque  complete ;  car  jusqu'  ici  les  cris- 
taux  entiers  de  Mica  et  cle  Talc  n'ont  pas  ete  fort  com- 
muns." 

These  inconveniencies  arise  from  neglecting  the  lead- 
ing rule  of  natural  history,  that  the  predominant  prin- 
ciple of  the  existence  of  an  object  must  determine  the 
Species;  whether  this  principle  be  reproduction  operating 
for  development,  or  crystallization  operating  for  perma- 
nence of  form.  We  may  add  to  the  above  statement  of 
inconveniencies  this ; — that  if  M.  Necker's  view  of  mine- 
ralogical  species  be  adopted,  the  distinction  of  species  is 
vague  and  indefinite,  while  that  of  genera  is  perfectly  pre- 
cise and  rigorous ; — an  aspect  of  the  system  entirely  at 
variance  with  other  parts  of  natural  history ;  for  in  all 
these  the  species  is  a  more  definite  group  than  the  genus. 

This  result  follows,  as  has  already  been  said,  from 
M.  Necker's  wish  to  have  individuals  marked  by  ex- 
ternal form.  If,  instead  of  this,  we  are  contented  to 
take  for  an  individual  that  portion  of  a  mass,  of  whatever 
form,  which  is  connected  by  the  continuous  influence  of 
the  same  crystalline  forces,  by  whatever  incidents  these 
forces  may  be  manifested,  (as  cleavage,  physical  and  opti- 
cal properties,)  our  mode  of  proceeding  avoids  all  the 
above  inconveniencies,  applies  alike  to  the  most  perfect 
and  most  imperfect  specimens,  and  gives  a  result  agree- 
able to  the  general  analogy  of  natural  history,  and  the 
rules  of  its  methods  f. 

*  Regne,  Mineral,  ii.  414. 

t  I  will  not  again  enter  into  tlie  subject  of  Nomenclature;  but  I 
may  remark  that  M.  Necker  has  adopted  (i.  415)  the  Nomenclature  of 
Beudant,  latinising  the  names,  and  thus  converting  each  into  a  single 
word.  He  has  also  introduced,  besides  the  names  of  Genera,  names  of 

2  L  2 


516         PHILOSOPHY  OF  THE  CLASSIFICATORY  SCIENCES. 

I  now  quit  the  subject  of  mere  Resemblance,  and  pro- 
ceed to  treat  of  that  natural  affinity  which  Natural 
Systems  of  Classification  for  organic  bodies  must  involve. 


CHAPTER  TV. 
OF  THE  IDEA  OF  NATURAL  AFFINITY. 

1.  IN  the  Second  Chapter  of  this  Book  it  was 
shown  that  although  the  Classificatory  Sciences  proceed 
ostensibly  upon  the  Idea  of  Resemblance  as  their  main 
foundation,  they  necessarily  take  for  granted  in  the 
course  of  their  progress  a  further  Idea  of  Natural  Affinity. 
This  appeared*  by  a  general  consideration  of  the  nature 
of  Science,  by  the  recognition  of  natural  species  and 
genera,  even  in  Artificial  Systems  of  Classification!,  and 
by  the  attempts  of  botanists  to  form  a  Natural  System. 
It  further  appeared  that  among  the  processes  by  which 
endeavours  have  been  made  to  frame  a  Natural  System, 
some,  as  the  method  of  blind  trial  and  the  method  or 
general  comparison,  have  been  altogether  unsuccessful; 
being  founded  only  upon  a  collection  of  resemblances, 
casual  in  the  one  case  and  arbitrary  in  the  other.  In 
neither  of  these  processes  is  there  employed  any  general 
principle  by  which  we  may  be  definitely  directed  as  to 
what  resemblances  we  should  employ,  or  by  which  the 
result  at  which  we  arrive  may  be  verified  and  confirmed. 
Our  object  in  the  present  chapter  is  to  show  that  the 
Idea  of  Natural  Affinity  supplies  us  with  a  principle 
which  may  answer  such  purposes. 

Families  taken  from  the  typical  Genus.     Thus  the  Family  of  Carlo- 
nidiens  contains  the  following  genera :   Calcispathum,  Magnesispathum, 
Dolomispathum,  Ferrispathum^  &c.,  Malachite,  Azuria.  Gaylusacia. 
*  Art.  5.  f  Art.  7- 


IDEA   OF   NATURAL   AFFINITY.  517 

I  shall  first  consider  the  Idea  of  Affinity  as  exempli- 
fied in  organized  beings.  In  doing  this,  we  may  appear 
to  take  for  granted  Ideas  which  have  not  yet  come  under 
our  discussion,  as  the  Ideas  of  Organization,  and  Vital 
Function  ;  but  it  will  be  found  that  the  principle  to  which 
we  are  led  is  independent  of  these  additional  Ideas. 

2.  We  have  already  seen  that  the  attempts  to  dis- 
cover the  divisions  which  result  from  this  Natural  Affinity 
have  led  to   the  consideration  of  the  Subordination  of 
Characters.     It  is  easy  to  see  that  some  organs  are  more 
essential  than  others  to  the  existence  of  an  organized 
being ;  the  organs  of  nutrition,  for  example,  more  essen- 
tial than  those  of  locomotion.     But  at  the  same  time  it 
is  clear  that  any  arbitrary  assumption  of  a  certain  scale 
of  relative  values  of  different  kinds  of  characters  will  lead 
only  to  an  Artificial  System.     This  will  happen,  if,  for 
example,  we  begin  by  declaring  the  nutritive  to  be  supe- 
rior in  importance  to  the  reproductive  functions.     It  is 
clear   that   this  relation   of  importance    of  organs  and 
functions  must  be  collected  by  the  study  of  the  organized 
beings ;    and  cannot  be  determined  a  priori,  without  de- 
priving us  of  all  right  to  expect  a  general  accordance 
between  our  system  and  the  arrangement  of  nature.     We 
see,  therefore,  that  our  notion  of  Natural  Affinity  involves 
in  it  this  consequence ; — that  it  is  not  to  be  made  out  by 
an  arbitrary  subordination  of  characters. 

3.  The  functions  and  actions  of  living  things  which 
we  separate  from  each  other  in  our  consideration,  cannot 
be  severed  in  nature.     Each  function  is  essential ;    Life 
implies  a  collection  of  movements,  and  ceases  when  any 
of  these  movements  is  stopped.     A  change  in  the  organi- 
zation subservient  to  one  set  of  functions  may  lead  neces- 
sarily to  a  change  in  the  organization  belonging  to  others. 
We  can  often  see  this  necessary  connexion ;   and  from  a 
comparison  of  the  forms  of  organized  beings,— from  the 


518        PHILOSOPHY  OF  THE  CLASSIFICATORY  SCIENCES. 

way  in  which  their  structure  changes  in  passing  from  one 
class  to  another,  we  are  led  to  the  conviction  that  there 
is  some  general  principle  which  connects  and  graduates 
all  such  changes.  When  the  circulatory  system  changes, 
the  nervous  system  changes  also:  when  the  mode  of 
locomotion  changes,  the  respiration  is  also  modified. 

4.  These  corresponding  changes  may  be  considered  as 
ways  in  which  the  living  thing  is  fitted  to  its  mode  of 
life ;  as  marks  of  adaptation  to  a  purpose ;  oi\  as  it  has 
been  otherwise  expressed,  as  results  of  the  conditions  of 
existence.  But  at  the  present  moment,  we  put  forward 
these  correspondencies  in  a  different  light.  We  adduce 
them  as  illustrations  of  what  we  mean  by  Affinity,  and 
what  we  consider  as  the  tendency  of  a  Natural  Classifi- 
cation. It  has  sometimes  been  asserted  that  if  we  were 
to  classify  any  of  the  departments  of  organized  nature  by 
means  of  one  function,  and  then  by  means  of  another,  the 
two  classifications,  if  each  strictly  consistent  with  itself, 
would  be  consistent  with  each  other.  Such  an  assertion 
is  perhaps  more  than  we  are  entitled  to  make  with  con- 
fideftce  ;  but  it  shows  very  well  what  is  meant  by  Affinity. 
The  disposition  to  believe  such  a  general  identity  of  all 
partial  natural  classifications,  shows  how  readily  we  fix 
upon  the  notion  of  Affinity,  as  general  result  of  the 
causes  which  determine  the  forms  of  living  things. 
When  these  causes  or  principles,  of  whatever  nature  they 
are  conceived  to  be,  vary  so  as  to  modify  one  part  of  the 
organization  of  the  being,  they  also  modify  another :  and 
thus  the  groups  which  exhibit  this  variation  of  the  funda- 
mental principles  of  form,  are  the  same,  whether  the 
manifestation  of  the  change  be  sought  in  one  part  or  in 
another  of  the  organized  structure.  The  groups  thus 
formed  are  related  by  Affinity ;  and  in  proportion  as  we 
find  the  evidence  of  more  functions  and  more  organs  to 
the  propriety  of  our  groups,  we  are  more  and  more  satis- 


IDEA  OF  NATU11AL  AFFINITY.  519 

fied  that  they  are  Natural  Classes.  It  appears,  then, 
that  our  Idea  of  Affinity  involves  the  conviction  of  the 
coincidence  of  natural  arrangements  formed  on  different 
functions ;  and  this,  rather  than  the  principle  of  the  sub- 
ordination of  some  characters  to  others,  is  the  true 
ground  of  the  natural  method  of  Classification. 

5.  For  example,  Cuvier,  after  speaking  of  the  Subor- 
dination of  Characters  as  the  guide  which  he  intends  to 
follow  in  his  arrangement  of  animals,  interprets  this 
principle  in  such  a  manner*  as  to  make  it  agree  nearly 
with  the  one  just  stated.  "In  pursuance  of  what  has 
been  said  on  methods  in  general,  wre  now  require  to 
know  what  characters  in  animals  are  the  most  influential, 
and  therefore  those  which  must  be  made  the  grounds  of 
the  primary  divisions."  "These,"  he  says,  "it  is  clear 
must  be  those  which  are  taken  from  the  animal  func- 
tions ; — sensation  and  motion  :" — But  how  does  he  con- 
firm this  ?  Not  by  showing  that  the  animal  functions 
are  independent  of,  or  predominant  over,  the  vegetative, 
but  by  observing  that  they  follow  the  same  gradations. 
"  Observation,"  he  continues,  "  confirms  this  view,  by 
showing  that  the  degrees  of  developement  and  compli- 
cation of  the  animal  functions  agree  with  those  of  the 
vegetative.  The  heart  and  the  organs  of  the  circulation 
are  a  sort  of  centre  for  the  vegetative  functions,  as  the 
brain  and  the  trunk  of  the  nervous  system  are  for  the 
animal  functions.  Now  we  see  these  two  systems  de- 
scend in  the  scale,  and  disappear  the  one  with  the  other. 
In  the  lowest  animals,  when  there  are  no  longer  any 
distinct  nerves,  there  are  also  no  longer  distinct  fibres, 
and  the  organs  of  digestion  are  simply  hollowed  out  in 
the  homogeneous  mass  of  the  body.  The  muscular  system 
disappears  even  before  the  nervous,  in  insects ;  but  in 
general  the  distribution  of  the  medullary  masses  corre- 

*  Reg-ne  Animal,  p.  55. 


520        PHILOSOPHY  OF  THE  CLASSIFICATORY  SCIENCES. 

spends  to  that  of  the  muscular  instruments ;  a  spinal  cord, 
on  which  knots  or  ganglions  represent  so  many  brains, 
corresponds  to  a  body  divided  into  numerous  rings  and 
supported  on  pairs  of  members  placed  at  different  points 
of  the  length,  and  so  on. 

"  This  correspondence  of  the  general  forms  which  result 
from  the  arrangement  of  the  motive  organs,  from  the  dis- 
tribution of  the  nervous  masses,  and  from  the  energy  of 
the  circulatory  system,  must  therefore  form  the  ground 
of  the  first  great  sections  by  which  we  divide  the  animal 
kingdom." 

6.  Decandolle  takes  the  same  view.  There  must  be, 
he  says,  an  equilibrium  of  the  different  functions^.  And 
he  exemplifies  this  by  the  case  of  the  distinction  of  mono- 
cotyledonous  and  dicotyledonous  plants,  which  being  at 
first  established  by  means  of  the  organs  of  reproduction, 
was  afterwards  found  to  coincide  with  the  distinction  of 
endogenous  and  exogenous,  which  depends  on  the  process 
of  nutrition.  "  Thus,"  he  adds,  "  the  natural  classes  founded 
on  one  of  the  great  functions  of  the  vegetable  are  necessarily 
the  same  as  those  which  are  founded  upon  the  other  func- 
tion ;  and  I  find  here  a  very  useful  criterion  to  ascertain 
whether  a  class  is  natural :  namely,  in  order  to  announce 
that  it  is  so,  it  must  be  arrived  at  by  the  two  roads 
which  vegetable  organization  presents.  Thus  I  affirm," 
he  says,  "  that  the  division  of  monocotyledons  from 
dicotyledons,  and  the  distinction  of  Grammes  from 
Cyperacese,  are  real,  because  in  these  cases,  I  arrive  at 
the  same  result  by  the  reproductive  and  the  nutritive 
organs ;  while  the  distinction  of  monopetalous  and  poly- 
petalous,  of  Rhodoracese  and  Ericinese  appears  to  me 
artificial,  because  I  can  arrive  at  it  only  by  the  reproduc- 
tive organs." 

Thus  the  correspondence  of  the  indications  of  different 
*  TL  El.,  p.  79. 


IDEA  OF  NATURAL  AFFINITY.  521 

functions  is  the  criterion  of  Natural  Classes ;  and  this 
correspondence  may  be  considered  as  one  of  the  best  and 
most  characteristic  marks  of  the  fundamental  Idea  of 
Affinity.  And  the  Maxim  by  which  all  Systems  professing 
to  be  natural  must  be  tested  is  this : — that  the  arrange- 
ment obtained  from  one  set  of  characters  coincides  with  the 
arrangement  obtained  from  another  set. 

This  Idea  of  Affinity,  as  a  natural  connexion  among 
various  species,  of  which  connexion  all  particular  resem- 
blances are  indications,  has  principally  influenced  the 
attempts  at  classifying  the  animal  kingdom.  The  reason 
why  the  classification  in  this  branch  of  Natural  History 
has  been  more  easy  and  certain  than  that  of  the  vegetable 
world  is,  as  Decandolle  says*,  that  besides  the  func- 
tions of  nutrition  and  reproduction,  which  animals  have 
in  common  with  plants,  they  have  also  in  addition  the 
function  of  sensation ;  and  thus  have  a  new  means  of 
verification  and  concordance.  But  we  may  add,  as  a 
further  reason,  that  the  functions  of  animals  are  necessa- 
rily much  more  obvious  and  intelligible  to  us  than  those 
of  vegetables,  from  their  clear  resemblance  to  the  opera- 
tions which  take  place  in  our  own  bodies,  to  which  our 
attention  has  necessarily  been  strongly  directed. 

7.  The  question  here  offers  itself,  whether  this  Idea 
of  Natural  Affinity  is  applicable  to  inorganic  as  well  as 
to  organic  bodies  ; — whether  there  be  Natural  Affinities 
among  Minerals.  And  to  this  we  are  now  enabled  to 
reply  by  considering  whether  or  not  the  principle  just 
stated  is  applicable  in  such  cases.  And  the  conclusion 
to  which  our  principle  leads  us  is, — that  there  are  such 
Natural  Affinities  among  Minerals,  since  there  are  dif- 
ferent sets  of  characters  which  may  be  taken,  (and  have 
by  different  writers  been  taken,)  as  the  basis  of  classifica- 
tion. The  hardness,  specific  gravity,  colour,  lustre, 

*  Th.  EL,  p.  80. 


522        PHILOSOPHY  OF  THE  CLASSIFICATORY  SCIENCES. 

crystallization,  and  other  external  characters,  as  they  are 
termed,  form  one  body  of  properties  according  to  which 
minerals  may  be  classified;  as  has  in  fact  been  done  by 
Molis,  Breithaupt,  and  others.  The  chemical  constitution 
of  the  substances,  on  the  other  hand,  may  be  made  the 
principle  of  their  arrangement,  as  was  done  by  Haiiy, 
and  more  recently,  and  on  a  different  scheme,  by  Ber- 
zelius.  Which  of  these  is  the  true  and  natural  classifica- 
tion ?  To  this  we  answer,  that  each  of  these  arrange- 
ments is  true  and  natural,  then,  and  then  only,  when  it 
coincides  with  the  other.  An  arrangement  by  external 
characters  which  gives  us  classes  possessing  a  common 
chemical  character;  —  a  chemical  order  which  brings 
together  like  and  separates  unlike  minerals ; — such  classi- 
fications have  the  evidence  of  truth  in  their  agreement 
with  one  another.  Every  classification  of  minerals  which 
does  not  aim  at  and  tend  to  such  a  result,  is  so  far  merely 
arbitrary ;  and  cannot  be  subservient  to  the  expression 
of  general  chemical  and  mineralogical  truths,  which  is  the 
proper  purpose  of  such  a  classification. 

8.  In  the  History  of  Mineralogy  I  have  related  the 
advances  which  have  been  made  among  mineralogists  and 
chemists  in  modern  times  towards  a  System  possessing 
this  character  of  truth.  I  have  there  described  the  mixed 
systems  of  Werner  and  Haiiy ; — the  attempt  made  by 
Mohs  to  form  a  pure  Natural  History  system ; — the  first 
and  second  attempt  of  Berzelius  to  form  a -pure  chemical 
system  ;  and  the  failure  of  both  these  attempts.  But  the 
distinct  separation  of  the  two  elements  of  which  science 
requires  the  coincidence  threw  a  very  useful  light  upon 
the  subject ;  and  the  succeeding  mixed  systems,  such  as 
that  of  Naumann,  approached  much  nearer  to  the  true 
conditions  of  the  problem  than  any  of  the  preceding  ones 
had  done.  Thus,  as  I  have  stated,  several  of  Naumann's 
groups  have  both  a  common  chemical  character  and  great 


IDEA  OF  NATURAL  AFFINITY.  523 

external  resemblances.  Such  are  \A*  Anhydrous  Unmetallic 
Haloids — his  Anhydrous  Metallic  Haloids — Hydrous  Metal- 
lic Haloids — Oxides  of  metals — Pyrites — Glances — Blendes. 
The  existence  of  such  groups  shows  that  we  may  hope 
ultimately  to  obtain  a  classification  of  minerals  which 
shall  be  both  chemically  significant  and  agreeable  to  the 
methods  of  Natural  History :  although,  when  we  consider 
how  very  imperfect  as  yet  our  knowledge  of  the  chemical 
composition  of  minerals  is,  we  can  hardly  flatter  ourselves 
that  we  shall  arrive  at  such  a  result  very  soon. 

We  have  thus  seen  that  in  Mineralogy,  as  well  as  in 
the  sciences  which  treat  of  organized  bodies,  we  may 
apply  the  Idea  of  Natural  Affinity ;  of  which  the  funda- 
mental maxim  is,  that  arrangements  obtained  from  different 
sets  of  characters  must  coincide. 

Since  the  notion  of  Affinity  is  thus  applicable  to 
inorganic  as  well  as  to  organic  bodies,  it  is  plain  that  it 
is  not  a  mere  modification  of  the  Idea  of  Organization  or 
Function,  although  it  may  in  some  of  its  aspects  appear  to 
approach  near  to  these  other  Ideas.  But  these  Ideas,  or 
others  which  are  the  foundation  of  them,  necessarily  enter 
in  a  very  prominent  and  fundamental  manner  into  all  the 
other  parts  of  Natural  History.  To  the  consideration  of 
these,  therefore,  we  shall  now  proceed. 


END  OF  THE  FIRST  VOLUME. 


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Hospital.     8s.  6d.  ;   and,  by  the  same  Author,  65.  6(7., 

MANAGEMENT  of  the  ORGANS  of  DIGESTION 

In  Health  and  Disease. 

MUSICAL  HISTORY,  BIOGRAPHY,  AND 
CRITICISM ; 

Being  a  General  Survey  of  Music  from  the  Earliest  to  the  Present  Time. 
By  GEORGE  HOGARTH.     In  Two  Volumes.     10*.  6d, 

STUDENT'S  MANUAL  OF  ANCIENT  HISTORY; 

Containing  the  Political  History,  Geographical  Position,  and  Social 

State  of  the  Principal  Nations  of  Antiquity. 
By  W.  C.  TAYLOR,  LL.D.,  M.R.A.S. ;  Trin.  Coll.,  Dublin. 

Also,  by  the  same  Author, 

STUDENT'S  MANUAL  OF  MODERN  HISTORY; 

The  Rise  and  Progress  of  the  principal  European  Nations,  their 

Political  History,  and  the  Changes  in  their  Social 

Condition. 

Each  Volume,  10s.  6d. 

The  contents  of  these  comprehensive  volumes  have  been  carefully  drawn  from  the 
•works  of  ancient  writers,  and  are  illustrated  by  the  discoveiies  of  modern  scholars  and 
travellers.  They  are  intended  to  supply  the  student  with  a  compendious  narrative  of  the 
principal  events  which  have  occurred  in  the  history  of  the  world,  and  to  lead  him  to  a  con- 
sideration of  the  causes  which  have  produced  the  principal  events  recorded.  The  geographi- 
cal position,  natural  productions,  and  progress  of  civilization  in  all  the  great  monarchies  and 
republics  have  been  diligently  investigated,  and  their  effects  on  the  fortunes  of  the  state 
pointed  out.  Thus  the  philosophy  of  history  is  made  to  illustrate  the  narrative  without 
interrupting  it. 

THE  STUDENT'S  MANUAL  OF  NATURAL 
PHILOSOPHY ; 

By  CHARLES  TOMLINSON. 

Comprising  Descriptions,  Popular  and  Practical,  of  the  most  important 
Philosophical  Instruments,  their  History,  Nature,  and  Uses. 

105.  6d. 
Dedicated,  by  permission,  to  the  Lord  Bishop  of  Salisbury. 

In  this  work  certain  prominent  subjects  have  been  selected  with  which  it  behoves  every 
one  to  be  acquainted ;  such,  for  example,  as  relate  to  what  may  be  called  our  HOUSEHOLD 
INSTRUMENTS,  namely, the  Thermometer,  the  Barometer,  and  Vernier ;  the  Hydrometer ;  the 
Hygrometer,  the  Tuning-Fork,  Musical  Glasses  and  Music  generally;  the  Compass;  the 
Prism,  the  Telescope,  and  the  Sun-Dial.  These  subjects,  and  those  in  immediate  connexion 
with  them,  are  treated  of  extensively ;  as  also  their  application  to  Science,  Art,  and  Industry. 


A  MANUAL  OF  CHEMISTRY. 

By  WILLIAM  THOS.  BRANDE,  F.R.S.,  of  Her  Majesty's  Mint. 

The  Fourth  Edition,  greatly  Enlarged,  and  with  numerous 

Wood-cuts,  30^. 

AN  INTRODUCTION  TO  THE  STUDY  OF 
CHEMICAL  PHILOSOPHY; 

By  J.  FREDERICK  DANIELL,  F.R.S.,  Professor  of  Chemistry  in 
King's  College,  London.     Octavo,  16s. 

A  DICTIONARY  OF  THE  MATERIA  MEDICA 
AND  PHARMACY; 

Including  the  Elements  of  Pharmaceutical  Chemistry,  and  a  Translation 

of  the  London  Pharmacopoeia. 

By  WILLIAM  THOS.  BRANDE,  Author  of  the  Manual  of 
Chemistry.     Octavo,  15s. 

RECREATIONS  IN  ASTRONOMY. 

By  Rev.  LEWIS  TOMLINSON,  M.A. 

With  many  Wood-cuts,  4s.  6d. 

A  popular  view  of  the  science  of  astronomy,  including  the  suhstance  of  several  chapters 
on  the  subject  that  appeared  in  the  Saturday  Magazine.  It  explains  the  laws  that  regulate 
the  planetary  system,  describes  the  different  planets,  and  treats  also  of  the  other  heavenly 
bodies,  of  the  telescope,  the  dial,  &c.  The  language  is  plain,  and  the  explanations  are 
made  clear  by  familiar  comparisons,  and  illustrated  by  numerous  diagrams  and  pictures, 
engraved  in  wood.  A  Glossary  of  terms  and  an  Index  are  appended;  and,  altogether,  this 
is  the  best  "Popular  Astronomy"  we  have  met  with. — Spectator. 

RECREATIONS  IN  GEOLOGY; 

With  an  Introductory  Discourse  on  the  Nature  and  Advantages  of 
the  Science,  and  a  copious  GLOSSARY. 

By  MISS  ZORNLIN. 
With  many  Wood-cuts,  4s.  6d. 

While  there  is  a  total  absence  of  pretension  in  the  general  form  and  style  of  the  volume, 
it  is  evident  that  a  great  deal  of  reading  and  research  have  been  requisite  for  its  production, 
and  that  the  authoress  must  have  turned  over  a  number  of  dry  and  ponderous  tomes,  the 
very  sight  of  which  would  scare  numbers  of  the  fair  sex.  *  *  *  Thus,  though  the 
book  is  short,  it  is  not  superficial,  and,  moreover,  the  authoress,  anxious  to  throw  light  on 
her  subject  from  every  side,  has  not  merely  confined  herself  to  geological  sources,  but  has 
brought  in  much  collateral  information,  chemical,  historical,  and  etymological.  With 
etymology  she  has  been  particularly  careful,  never  introducing  an  unusual  technical  expres- 
sion, without  giving  its  Greek  or  Latin  origin.  *  *  *  While  the  work  is  excellently 
put  together  as  a  whole,  a  very  copious  Index  renders  easy  a  reference  to  any  part.  A 
Glossary  is  also  added,  which  explains  all  the  technical  words,  and  thus  the  book  contains  all 
that  those  would  desire  to  know  whose  occupations  or  inclinations  hinder  them  from  pursuing 
geology  to  any  great  extent,  and  are  at  the  same  time  desirous  of  knowing  what  their  geolo- 
gical contemporaries  are  about.  It  will  also  be  an  agreeable  pocket  volume  for  the  tourist, 
who  may  be  anxious  to  know  something  concerning  the  various  soils  over  which  he  passes. 
— Times. 

I